Cheng, Juan; Lei, Nuo; Shu, Chi-Wang High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics. (English) Zbl 07807997 J. Comput. Phys. 496, Article ID 112595, 29 p. (2024). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{J. Cheng} et al., J. Comput. Phys. 496, Article ID 112595, 29 p. (2024; Zbl 07807997) Full Text: DOI
Gu, Xiaolu; Cheng, Juan; Shu, Chi-Wang A high order positivity-preserving discontinuous Galerkin remapping method based on a moving mesh solver for ALE simulation of the compressible fluid flow. (English) Zbl 07787318 Commun. Comput. Phys. 34, No. 5, 1177-1214 (2023). MSC: 65M60 35Q31 PDFBibTeX XMLCite \textit{X. Gu} et al., Commun. Comput. Phys. 34, No. 5, 1177--1214 (2023; Zbl 07787318) Full Text: DOI
Borges, Rafael B.deR.; Colman, Flávio C.; da Silva, Nicholas D. P.; Dicati, Gabriela W. O.; Gubaua, José E.; Shu, Chi-Wang Approximated decompositions for computational continuum mechanics. (English) Zbl 07766264 J. Comput. Phys. 495, Article ID 112576, 15 p. (2023). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{R. B. deR. Borges} et al., J. Comput. Phys. 495, Article ID 112576, 15 p. (2023; Zbl 07766264) Full Text: DOI
Xu, Ziyao; Shu, Chi-Wang On the conservation property of positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations. (English) Zbl 07715234 J. Comput. Phys. 490, Article ID 112304, 31 p. (2023). MSC: 65Mxx 35Lxx 65Nxx PDFBibTeX XMLCite \textit{Z. Xu} and \textit{C.-W. Shu}, J. Comput. Phys. 490, Article ID 112304, 31 p. (2023; Zbl 07715234) Full Text: DOI
Lei, Nuo; Cheng, Juan; Shu, Chi-Wang A high order positivity-preserving polynomial projection remapping method. (English) Zbl 07640575 J. Comput. Phys. 474, Article ID 111826, 29 p. (2023). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{N. Lei} et al., J. Comput. Phys. 474, Article ID 111826, 29 p. (2023; Zbl 07640575) Full Text: DOI
Fan, Haitao; Shu, Chi-Wang High order numerical methods for flows with hysteretic fluxes. (English) Zbl 1506.65121 Appl. Numer. Math. 184, 234-252 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 65N06 65L06 90B20 76S05 76T06 76L05 35Q90 35Q35 PDFBibTeX XMLCite \textit{H. Fan} and \textit{C.-W. Shu}, Appl. Numer. Math. 184, 234--252 (2023; Zbl 1506.65121) Full Text: DOI
Gu, Xiaolu; Li, Yue; Cheng, Juan; Shu, Chi-Wang A high order positivity-preserving conservative WENO remapping method based on a moving mesh solver. (English) Zbl 07625423 J. Comput. Phys. 473, Article ID 111754, 25 p. (2023). MSC: 65Mxx 76Mxx 76Nxx PDFBibTeX XMLCite \textit{X. Gu} et al., J. Comput. Phys. 473, Article ID 111754, 25 p. (2023; Zbl 07625423) Full Text: DOI
Shu, Chi-Wang Inverse Lax-Wendroff boundary treatment: a survey. (English) Zbl 1524.65395 Commun. Math. Res. 38, No. 3, 333-350 (2022). MSC: 65M06 65M12 65M50 35F30 PDFBibTeX XMLCite \textit{C.-W. Shu}, Commun. Math. Res. 38, No. 3, 333--350 (2022; Zbl 1524.65395) Full Text: DOI
Amat, Sergio; Ruiz-Álvarez, Juan; Shu, Chi-Wang; Yáñez, Dionisio F. On the approximation of derivative values using a WENO algorithm with progressive order of accuracy close to discontinuities. (English) Zbl 1513.65274 Comput. Appl. Math. 41, No. 6, Paper No. 297, 38 p. (2022). MSC: 65M06 PDFBibTeX XMLCite \textit{S. Amat} et al., Comput. Appl. Math. 41, No. 6, Paper No. 297, 38 p. (2022; Zbl 1513.65274) Full Text: DOI
Araki, Luciano K.; Borges, Rafael B. de R.; da Silva, Nicholas Dicati P.; Shu, Chi-Wang High-resolution ILW outflow boundary treatment for the Navier-Stokes equations. (English) Zbl 1521.76765 Comput. Fluids 242, Article ID 105506, 11 p. (2022). MSC: 76N06 76M20 65M06 PDFBibTeX XMLCite \textit{L. K. Araki} et al., Comput. Fluids 242, Article ID 105506, 11 p. (2022; Zbl 1521.76765) Full Text: DOI
Xu, Ziyao; Shu, Chi-Wang High order conservative positivity-preserving discontinuous Galerkin method for stationary hyperbolic equations. (English) Zbl 07561087 J. Comput. Phys. 466, Article ID 111410, 26 p. (2022). MSC: 65Mxx 35Lxx 76Mxx PDFBibTeX XMLCite \textit{Z. Xu} and \textit{C.-W. Shu}, J. Comput. Phys. 466, Article ID 111410, 26 p. (2022; Zbl 07561087) Full Text: DOI
Lei, Nuo; Cheng, Juan; Shu, Chi-Wang A high order positivity-preserving conservative WENO remapping method on 3D tetrahedral meshes. (English) Zbl 1507.65267 Comput. Methods Appl. Mech. Eng. 395, Article ID 115037, 19 p. (2022). MSC: 65N50 65M50 PDFBibTeX XMLCite \textit{N. Lei} et al., Comput. Methods Appl. Mech. Eng. 395, Article ID 115037, 19 p. (2022; Zbl 1507.65267) Full Text: DOI
Lei, Nuo; Cheng, Juan; Shu, Chi-Wang High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model. (English) Zbl 07518051 J. Comput. Phys. 454, Article ID 110945, 34 p. (2022). MSC: 65Mxx 35Lxx 35Qxx PDFBibTeX XMLCite \textit{N. Lei} et al., J. Comput. Phys. 454, Article ID 110945, 34 p. (2022; Zbl 07518051) Full Text: DOI
Li, Tingting; Lu, Jianfang; Shu, Chi-Wang Stability analysis of inverse Lax-Wendroff boundary treatment of high order compact difference schemes for parabolic equations. (English) Zbl 1481.65145 J. Comput. Appl. Math. 400, Article ID 113711, 26 p. (2022). MSC: 65M06 65L06 65M20 65N25 65M12 35K10 PDFBibTeX XMLCite \textit{T. Li} et al., J. Comput. Appl. Math. 400, Article ID 113711, 26 p. (2022; Zbl 1481.65145) Full Text: DOI
Lei, Nuo; Cheng, Juan; Shu, Chi-Wang A high order positivity-preserving conservative WENO remapping method on 2D quadrilateral meshes. (English) Zbl 1506.65126 Comput. Methods Appl. Mech. Eng. 373, Article ID 113497, 29 p. (2021). MSC: 65M06 PDFBibTeX XMLCite \textit{N. Lei} et al., Comput. Methods Appl. Mech. Eng. 373, Article ID 113497, 29 p. (2021; Zbl 1506.65126) Full Text: DOI
Cheng, Juan; Shu, Chi-Wang; Song, Peng High order conservative Lagrangian schemes for one-dimensional radiation hydrodynamics equations in the equilibrium-diffusion limit. (English) Zbl 07508352 J. Comput. Phys. 421, Article ID 109724, 24 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{J. Cheng} et al., J. Comput. Phys. 421, Article ID 109724, 24 p. (2020; Zbl 07508352) Full Text: DOI
Zhu, Jun; Shu, Chi-Wang Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study. (English) Zbl 1476.65200 Commun. Appl. Math. Comput. 2, No. 3, 429-460 (2020). MSC: 65M06 35L65 PDFBibTeX XMLCite \textit{J. Zhu} and \textit{C.-W. Shu}, Commun. Appl. Math. Comput. 2, No. 3, 429--460 (2020; Zbl 1476.65200) Full Text: DOI
Amat, Sergio P.; Ruiz, Juan; Shu, Chi-Wang; Yáñez, Dionisio F. A new WENO-\(2r\) algorithm with progressive order of accuracy close to discontinuities. (English) Zbl 1457.65038 SIAM J. Numer. Anal. 58, No. 6, 3448-3474 (2020). MSC: 65M06 65D05 41A05 41A10 PDFBibTeX XMLCite \textit{S. P. Amat} et al., SIAM J. Numer. Anal. 58, No. 6, 3448--3474 (2020; Zbl 1457.65038) Full Text: DOI arXiv
Tao, Qi; Xu, Yan; Shu, Chi-Wang An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives. (English) Zbl 1446.65118 Math. Comput. 89, No. 326, 2753-2783 (2020). MSC: 65M60 65M15 65M12 35G25 PDFBibTeX XMLCite \textit{Q. Tao} et al., Math. Comput. 89, No. 326, 2753--2783 (2020; Zbl 1446.65118) Full Text: DOI arXiv
Ding, Shengrong; Shu, Chi-Wang; Zhang, Mengping On the conservation of finite difference WENO schemes in non-rectangular domains using the inverse Lax-Wendroff boundary treatments. (English) Zbl 1440.65086 J. Comput. Phys. 415, Article ID 109516, 32 p. (2020). MSC: 65M06 35L65 76M20 76L05 PDFBibTeX XMLCite \textit{S. Ding} et al., J. Comput. Phys. 415, Article ID 109516, 32 p. (2020; Zbl 1440.65086) Full Text: DOI
Wu, Kailiang; Shu, Chi-Wang Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations. (English) Zbl 1450.65089 SIAM J. Sci. Comput. 42, No. 4, A2230-A2261 (2020). Reviewer: Qifeng Zhang (Hangzhou) MSC: 65M06 65M12 76W05 76Y05 76M20 35L65 35Q35 PDFBibTeX XMLCite \textit{K. Wu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 42, No. 4, A2230--A2261 (2020; Zbl 1450.65089) Full Text: DOI arXiv
Li, Yue; Cheng, Juan; Xia, Yinhua; Shu, Chi-Wang On moving mesh WENO schemes with characteristic boundary conditions for Hamilton-Jacobi equations. (English) Zbl 1519.65020 Comput. Fluids 205, Article ID 104582, 14 p. (2020). MSC: 65M06 65M25 PDFBibTeX XMLCite \textit{Y. Li} et al., Comput. Fluids 205, Article ID 104582, 14 p. (2020; Zbl 1519.65020) Full Text: DOI
Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang On a new WENO algorithm of order \(2r\) with improved accuracy close to discontinuities. (English) Zbl 1503.65161 Appl. Math. Lett. 105, Article ID 106298, 12 p. (2020). MSC: 65M06 35L65 65M12 PDFBibTeX XMLCite \textit{S. Amat} et al., Appl. Math. Lett. 105, Article ID 106298, 12 p. (2020; Zbl 1503.65161) Full Text: DOI
Mazaheri, Alireza; Shu, Chi-Wang; Perrier, Vincent Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements. (English) Zbl 1452.76097 J. Comput. Phys. 395, 461-488 (2019). MSC: 76M10 76N15 65M60 PDFBibTeX XMLCite \textit{A. Mazaheri} et al., J. Comput. Phys. 395, 461--488 (2019; Zbl 1452.76097) Full Text: DOI HAL
Zhu, Jun; Shu, Chi-Wang A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes. (English) Zbl 1452.76143 J. Comput. Phys. 392, 19-33 (2019). MSC: 76M12 65M08 35L65 PDFBibTeX XMLCite \textit{J. Zhu} and \textit{C.-W. Shu}, J. Comput. Phys. 392, 19--33 (2019; Zbl 1452.76143) Full Text: DOI
Wu, Kailiang; Shu, Chi-Wang Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. (English) Zbl 1419.76446 Numer. Math. 142, No. 4, 995-1047 (2019). MSC: 76M10 76M12 65M60 65M08 65M06 35L65 76W05 PDFBibTeX XMLCite \textit{K. Wu} and \textit{C.-W. Shu}, Numer. Math. 142, No. 4, 995--1047 (2019; Zbl 1419.76446) Full Text: DOI arXiv
Shu, Chi-Wang Bound-preserving high-order schemes for hyperbolic equations: survey and recent developments. (English) Zbl 1412.65155 Klingenberg, Christian (ed.) et al., Theory, numerics and applications of hyperbolic problems II, Aachen, Germany, August 2016. Cham: Springer. Springer Proc. Math. Stat. 237, 591-603 (2018). MSC: 65M60 65M08 65M06 35B50 76Y05 35Q31 PDFBibTeX XMLCite \textit{C.-W. Shu}, Springer Proc. Math. Stat. 237, 591--603 (2018; Zbl 1412.65155) Full Text: DOI
Du, Jie; Shu, Chi-Wang Positivity-preserving high-order schemes for conservation laws on arbitrarily distributed point clouds with a simple WENO limiter. (English) Zbl 1414.65012 Int. J. Numer. Anal. Model. 15, No. 1-2, 1-25 (2018). Reviewer: Vanja Nikolić (Garching) MSC: 65M12 65M15 65M60 76M10 35Q31 76N15 35L65 PDFBibTeX XMLCite \textit{J. Du} and \textit{C.-W. Shu}, Int. J. Numer. Anal. Model. 15, No. 1--2, 1--25 (2018; Zbl 1414.65012) Full Text: Link
Ling, Dan; Cheng, Juan; Shu, Chi-Wang Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations. (English) Zbl 1407.65196 J. Sci. Comput. 77, No. 3, 1801-1831 (2018). MSC: 65M60 65M06 65N30 65M12 35B09 35R09 80A20 35Q79 85A25 PDFBibTeX XMLCite \textit{D. Ling} et al., J. Sci. Comput. 77, No. 3, 1801--1831 (2018; Zbl 1407.65196) Full Text: DOI
Wu, Kailiang; Shu, Chi-Wang A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. (English) Zbl 1404.65184 SIAM J. Sci. Comput. 40, No. 5, B1302-B1329 (2018). MSC: 65M60 35L65 65M08 76W05 76M10 PDFBibTeX XMLCite \textit{K. Wu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 40, No. 5, B1302--B1329 (2018; Zbl 1404.65184) Full Text: DOI arXiv
Huang, Juntao; Shu, Chi-Wang Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms. (English) Zbl 1422.65259 J. Comput. Phys. 361, 111-135 (2018). MSC: 65M60 65L06 35L02 PDFBibTeX XMLCite \textit{J. Huang} and \textit{C.-W. Shu}, J. Comput. Phys. 361, 111--135 (2018; Zbl 1422.65259) Full Text: DOI
Fu, Guosheng; Shu, Chi-Wang A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. (English) Zbl 1380.65262 J. Comput. Phys. 347, 305-327 (2017). MSC: 65M60 35L65 76M10 PDFBibTeX XMLCite \textit{G. Fu} and \textit{C.-W. Shu}, J. Comput. Phys. 347, 305--327 (2017; Zbl 1380.65262) Full Text: DOI
Liu, Yuan; Cheng, Yingda; Shu, Chi-Wang A simple bound-preserving sweeping technique for conservative numerical approximations. (English) Zbl 1381.65087 J. Sci. Comput. 73, No. 2-3, 1028-1071 (2017). MSC: 65M70 35L65 65M06 65M08 35Q35 PDFBibTeX XMLCite \textit{Y. Liu} et al., J. Sci. Comput. 73, No. 2--3, 1028--1071 (2017; Zbl 1381.65087) Full Text: DOI
Shu, Chi-Wang A brief survey on high order numerical methods for convection dominated problems. (English) Zbl 1380.65182 Lin, Chang-Shou (ed.) et al., Proceedings of the sixth international congress of Chinese mathematicians, ICCM 2013, Taipei, Taiwan, July 14–19, 2013. Volume I. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-348-7/pbk; 978-1-57146-350-0/set). Advanced Lectures in Mathematics (ALM) 36, 119-133 (2017). MSC: 65M06 65M60 65M70 PDFBibTeX XMLCite \textit{C.-W. Shu}, Adv. Lect. Math. (ALM) 36, 119--133 (2017; Zbl 1380.65182)
Shu, Chi-Wang Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. (English) Zbl 1372.65251 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – methods and theoretical aspects. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57396-0/hbk; 978-3-319-57397-7/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 199, 3-14 (2017). MSC: 65M08 65M12 76M12 PDFBibTeX XMLCite \textit{C.-W. Shu}, Springer Proc. Math. Stat. 199, 3--14 (2017; Zbl 1372.65251) Full Text: DOI
Li, Tingting; Shu, Chi-Wang; Zhang, Mengping Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations. (English) Zbl 1361.65062 J. Sci. Comput. 70, No. 2, 576-607 (2017). MSC: 65M12 65M06 35K05 65M20 65L06 PDFBibTeX XMLCite \textit{T. Li} et al., J. Sci. Comput. 70, No. 2, 576--607 (2017; Zbl 1361.65062) Full Text: DOI
Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. II: The two-dimensional case. (English) Zbl 1351.76128 J. Comput. Phys. 312, 416-442 (2016). MSC: 76M12 65M08 76N15 PDFBibTeX XMLCite \textit{F. Vilar} et al., J. Comput. Phys. 312, 416--442 (2016; Zbl 1351.76128) Full Text: DOI
Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. I: The one-dimensional case. (English) Zbl 1351.76127 J. Comput. Phys. 312, 385-415 (2016). MSC: 76M12 65M08 76N15 PDFBibTeX XMLCite \textit{F. Vilar} et al., J. Comput. Phys. 312, 385--415 (2016; Zbl 1351.76127) Full Text: DOI
Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations. (English) Zbl 1349.65319 J. Comput. Phys. 317, 276-300 (2016). MSC: 65M06 PDFBibTeX XMLCite \textit{J. Lu} et al., J. Comput. Phys. 317, 276--300 (2016; Zbl 1349.65319) Full Text: DOI
Shu, Chi-Wang High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments. (English) Zbl 1349.65486 J. Comput. Phys. 316, 598-613 (2016). MSC: 65M60 65M08 65M12 PDFBibTeX XMLCite \textit{C.-W. Shu}, J. Comput. Phys. 316, 598--613 (2016; Zbl 1349.65486) Full Text: DOI
Du, Jie; Shu, Chi-Wang A high order stable conservative method for solving hyperbolic conservation laws on arbitrarily distributed point clouds. (English) Zbl 1351.65075 SIAM J. Sci. Comput. 38, No. 5, A3094-A3128 (2016). MSC: 65M60 65M50 35L65 76N15 76M10 PDFBibTeX XMLCite \textit{J. Du} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 38, No. 5, A3094--A3128 (2016; Zbl 1351.65075) Full Text: DOI
Yuan, Daming; Cheng, Juan; Shu, Chi-Wang High order positivity-preserving discontinuous Galerkin methods for radiative transfer equations. (English) Zbl 1351.65105 SIAM J. Sci. Comput. 38, No. 5, A2987-A3019 (2016). MSC: 65R20 45K05 82D75 85A25 PDFBibTeX XMLCite \textit{D. Yuan} et al., SIAM J. Sci. Comput. 38, No. 5, A2987--A3019 (2016; Zbl 1351.65105) Full Text: DOI
Li, Tingting; Shu, Chi-Wang; Zhang, Mengping Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes. (English) Zbl 1333.65101 J. Comput. Appl. Math. 299, 140-158 (2016). MSC: 65M12 65M06 35L65 65M20 65L06 PDFBibTeX XMLCite \textit{T. Li} et al., J. Comput. Appl. Math. 299, 140--158 (2016; Zbl 1333.65101) Full Text: DOI
Liu, Xuliang; Zhang, Shuhai; Zhang, Hanxin; Shu, Chi-Wang A new class of central compact schemes with spectral-like resolution. II: Hybrid weighted nonlinear schemes. (English) Zbl 1351.76170 J. Comput. Phys. 284, 133-154 (2015). MSC: 76M20 65M06 76L05 PDFBibTeX XMLCite \textit{X. Liu} et al., J. Comput. Phys. 284, 133--154 (2015; Zbl 1351.76170) Full Text: DOI
Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation. (English) Zbl 1349.76159 J. Comput. Phys. 298, 161-175 (2015). MSC: 76L05 65M06 65M50 PDFBibTeX XMLCite \textit{C. Wang} et al., J. Comput. Phys. 298, 161--175 (2015; Zbl 1349.76159) Full Text: DOI
Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates. (English) Zbl 1318.65051 Math. Models Methods Appl. Sci. 25, No. 8, 1553-1588 (2015). Reviewer: Yajuan Sun (Beijing) MSC: 65M06 65M12 65M15 60G50 35L67 PDFBibTeX XMLCite \textit{Y. Jiang} et al., Math. Models Methods Appl. Sci. 25, No. 8, 1553--1588 (2015; Zbl 1318.65051) Full Text: DOI
Cheng, Juan; Shu, Chi-Wang Positivity-preserving Lagrangian scheme for multi-material compressible flow. (English) Zbl 1349.76439 J. Comput. Phys. 257, Part A, 143-168 (2014). MSC: 76M20 65M06 76K05 76N99 PDFBibTeX XMLCite \textit{J. Cheng} and \textit{C.-W. Shu}, J. Comput. Phys. 257, Part A, 143--168 (2014; Zbl 1349.76439) Full Text: DOI
Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping Free-stream preserving finite difference schemes on curvilinear meshes. (English) Zbl 1292.65091 Methods Appl. Anal. 21, No. 1, 1-30 (2014). MSC: 65M06 65M50 35L65 PDFBibTeX XMLCite \textit{Y. Jiang} et al., Methods Appl. Anal. 21, No. 1, 1--30 (2014; Zbl 1292.65091) Full Text: DOI
Liu, Xuliang; Zhang, Shuhai; Zhang, Hanxin; Shu, Chi-Wang A new class of central compact schemes with spectral-like resolution. I: Linear schemes. (English) Zbl 1349.76504 J. Comput. Phys. 248, 235-256 (2013). MSC: 76M20 65M06 76G25 PDFBibTeX XMLCite \textit{X. Liu} et al., J. Comput. Phys. 248, 235--256 (2013; Zbl 1349.76504) Full Text: DOI
Yee, H. C.; Kotov, D. V.; Wang, Wei; Shu, Chi-Wang Spurious behavior of shock-capturing methods by the fractional step approach: problems containing stiff source terms and discontinuities. (English) Zbl 1349.80048 J. Comput. Phys. 241, 266-291 (2013). MSC: 80M25 80A25 76L05 PDFBibTeX XMLCite \textit{H. C. Yee} et al., J. Comput. Phys. 241, 266--291 (2013; Zbl 1349.80048) Full Text: DOI Link
Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. (English) Zbl 1311.76088 J. Comput. Phys. 242, 169-180 (2013). MSC: 76M20 65M06 35Q31 76N15 PDFBibTeX XMLCite \textit{X. Y. Hu} et al., J. Comput. Phys. 242, 169--180 (2013; Zbl 1311.76088) Full Text: DOI arXiv
Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping An alternative formulation of finite difference weighted ENO schemes with Lax-Wendroff time discretization for conservation laws. (English) Zbl 1266.65144 SIAM J. Sci. Comput. 35, No. 2, A1137-A1160 (2013). MSC: 65M06 PDFBibTeX XMLCite \textit{Y. Jiang} et al., SIAM J. Sci. Comput. 35, No. 2, A1137--A1160 (2013; Zbl 1266.65144) Full Text: DOI
Xiong, Tao; Shu, Chi-Wang; Zhang, Mengping WENO scheme with subcell resolution for computing nonconservative Euler equations with applications to one-dimensional compressible two-medium flows. (English) Zbl 1383.76359 J. Sci. Comput. 53, No. 1, 222-247 (2012). MSC: 76M12 76M28 65M70 PDFBibTeX XMLCite \textit{T. Xiong} et al., J. Sci. Comput. 53, No. 1, 222--247 (2012; Zbl 1383.76359) Full Text: DOI
Zhang, Xiangxiong; Liu, Yuanyuan; Shu, Chi-Wang Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes for convection-diffusion equations. (English) Zbl 1252.65146 SIAM J. Sci. Comput. 34, No. 2, A627-A658 (2012). MSC: 65M06 65M60 65M12 PDFBibTeX XMLCite \textit{X. Zhang} et al., SIAM J. Sci. Comput. 34, No. 2, A627--A658 (2012; Zbl 1252.65146) Full Text: DOI Link
Wang, Cheng; Zhang, Xiangxiong; Shu, Chi-Wang; Ning, Jianguo Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. (English) Zbl 1243.80011 J. Comput. Phys. 231, No. 2, 653-665 (2012). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 80A25 76J20 80A32 35Q31 65N30 PDFBibTeX XMLCite \textit{C. Wang} et al., J. Comput. Phys. 231, No. 2, 653--665 (2012; Zbl 1243.80011) Full Text: DOI
Zhang, Xiangxiong; Xia, Yinhua; Shu, Chi-Wang Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes. (English) Zbl 1247.65131 J. Sci. Comput. 50, No. 1, 29-62 (2012). Reviewer: Petr Sváček (Praha) MSC: 65M60 65M08 65M12 35L65 76N15 76D05 76M10 76M12 35B50 65M50 PDFBibTeX XMLCite \textit{X. Zhang} et al., J. Sci. Comput. 50, No. 1, 29--62 (2012; Zbl 1247.65131) Full Text: DOI
Zhang, Xiangxiong; Shu, Chi-Wang Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. (English) Zbl 1426.76493 J. Comput. Phys. 231, No. 5, 2245-2258 (2012). MSC: 76M20 76N15 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{C.-W. Shu}, J. Comput. Phys. 231, No. 5, 2245--2258 (2012; Zbl 1426.76493) Full Text: DOI
Xu, Yan; Shu, Chi-Wang Optimal error estimates of the semidiscrete local discontinuous Galerkin methods for high order wave equations. (English) Zbl 1247.65121 SIAM J. Numer. Anal. 50, No. 1, 79-104 (2012). Reviewer: Fernando Casas (Castellon) MSC: 65M15 65M60 65M20 65M12 35L25 35Q41 PDFBibTeX XMLCite \textit{Y. Xu} and \textit{C.-W. Shu}, SIAM J. Numer. Anal. 50, No. 1, 79--104 (2012; Zbl 1247.65121) Full Text: DOI
Zhang, Xiangxiong; Shu, Chi-Wang Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. (English) Zbl 1222.65107 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2134, 2752-2776 (2011). MSC: 65M60 65M12 35L65 35Q35 35B50 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{C.-W. Shu}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2134, 2752--2776 (2011; Zbl 1222.65107) Full Text: DOI
Xing, Yulong; Shu, Chi-Wang; Noelle, Sebastian On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations. (English) Zbl 1409.76086 J. Sci. Comput. 48, No. 1-3, 339-349 (2011). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{Y. Xing} et al., J. Sci. Comput. 48, No. 1--3, 339--349 (2011; Zbl 1409.76086) Full Text: DOI arXiv
Wang, Wei; Yee, H. C.; Sjögreen, Björn; Magin, Thierry; Shu, Chi-Wang Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows. (English) Zbl 1343.76037 J. Comput. Phys. 230, No. 11, 4316-4335 (2011). MSC: 76M20 65M06 PDFBibTeX XMLCite \textit{W. Wang} et al., J. Comput. Phys. 230, No. 11, 4316--4335 (2011; Zbl 1343.76037) Full Text: DOI Link
Zhang, Xiangxiong; Shu, Chi-Wang Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms. (English) Zbl 1391.76375 J. Comput. Phys. 230, No. 4, 1238-1248 (2011). MSC: 76M10 76M12 65M70 35Q35 65M08 76N15 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{C.-W. Shu}, J. Comput. Phys. 230, No. 4, 1238--1248 (2011; Zbl 1391.76375) Full Text: DOI
Xu, Yan; Shu, Chi-Wang Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. (English) Zbl 1364.65205 Commun. Comput. Phys. 7, No. 1, 1-46 (2010). MSC: 65M60 PDFBibTeX XMLCite \textit{Y. Xu} and \textit{C.-W. Shu}, Commun. Comput. Phys. 7, No. 1, 1--46 (2010; Zbl 1364.65205) Full Text: DOI
Zhang, Xiangxiong; Shu, Chi-Wang A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws. (English) Zbl 1226.65083 SIAM J. Numer. Anal. 48, No. 2, 772-795 (2010). Reviewer: R. K. Mohanty (Delhi) MSC: 65M08 35L65 35B50 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{C.-W. Shu}, SIAM J. Numer. Anal. 48, No. 2, 772--795 (2010; Zbl 1226.65083) Full Text: DOI Link
Zhang, Xiangxiong; Shu, Chi-Wang On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. (English) Zbl 1282.76128 J. Comput. Phys. 229, No. 23, 8918-8934 (2010). MSC: 76M10 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{C.-W. Shu}, J. Comput. Phys. 229, No. 23, 8918--8934 (2010; Zbl 1282.76128) Full Text: DOI
Zhang, Xiangxiong; Shu, Chi-Wang On maximum-principle-satisfying high order schemes for scalar conservation laws. (English) Zbl 1187.65096 J. Comput. Phys. 229, No. 9, 3091-3120 (2010). MSC: 65M08 65M06 65M60 65M12 35L65 35B50 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{C.-W. Shu}, J. Comput. Phys. 229, No. 9, 3091--3120 (2010; Zbl 1187.65096) Full Text: DOI
Zhang, Yong-Tao; Shu, Chi-Wang Third order WENO scheme on three dimensional tetrahedral meshes. (English) Zbl 1364.65177 Commun. Comput. Phys. 5, No. 2-4, 836-848 (2009). MSC: 65M08 PDFBibTeX XMLCite \textit{Y.-T. Zhang} and \textit{C.-W. Shu}, Commun. Comput. Phys. 5, No. 2--4, 836--848 (2009; Zbl 1364.65177)
Abgrall, Remi; Shu, Chi-Wang Development of residual distribution schemes for the discontinuous Galerkin method: the scalar case with linear elements. (English) Zbl 1364.65190 Commun. Comput. Phys. 5, No. 2-4, 376-390 (2009). MSC: 65M60 PDFBibTeX XMLCite \textit{R. Abgrall} and \textit{C.-W. Shu}, Commun. Comput. Phys. 5, No. 2--4, 376--390 (2009; Zbl 1364.65190)
Noelle, Sebastian; Xing, Yulong; Shu, Chi-Wang High-order well-balanced schemes. (English) Zbl 1266.65147 Puppo, Gabriella (ed.) et al., Numerical methods for balance laws. Caserta: Dipartimento di Matematica, Seconda Università di Napoli (ISBN 978-88-548-3360-9/hbk). Quaderni di Matematica 24, 1-66 (2009). MSC: 65M06 65M08 65M60 35L65 65M15 76B15 76M10 76M12 76M20 PDFBibTeX XMLCite \textit{S. Noelle} et al., Quad. Mat. 24, 1--66 (2009; Zbl 1266.65147)
Gottlieb, Sigal; Ketcheson, David I.; Shu, Chi-Wang High order strong stability preserving time discretizations. (English) Zbl 1203.65135 J. Sci. Comput. 38, No. 3, 251-289 (2009). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{S. Gottlieb} et al., J. Sci. Comput. 38, No. 3, 251--289 (2009; Zbl 1203.65135) Full Text: DOI
Liu, Wei; Cheng, Juan; Shu, Chi-Wang High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations. (English) Zbl 1287.76181 J. Comput. Phys. 228, No. 23, 8872-8891 (2009). MSC: 76M20 65M06 PDFBibTeX XMLCite \textit{W. Liu} et al., J. Comput. Phys. 228, No. 23, 8872--8891 (2009; Zbl 1287.76181) Full Text: DOI
Cheng, Juan; Shu, Chi-Wang A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations. (English) Zbl 1364.76111 Commun. Comput. Phys. 4, No. 5, 1008-1024 (2008). MSC: 76M12 65N06 35Q31 PDFBibTeX XMLCite \textit{J. Cheng} and \textit{C.-W. Shu}, Commun. Comput. Phys. 4, No. 5, 1008--1024 (2008; Zbl 1364.76111)
Qiu, Jing-Mei; Shu, Chi-Wang Convergence of Godunov-type schemes for scalar conservation laws under large time steps. (English) Zbl 1176.65096 SIAM J. Numer. Anal. 46, No. 5, 2211-2237 (2008). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{J.-M. Qiu} and \textit{C.-W. Shu}, SIAM J. Numer. Anal. 46, No. 5, 2211--2237 (2008; Zbl 1176.65096) Full Text: DOI Link
Cheng, Juan; Shu, Chi-Wang A high order accurate conservative remapping method on staggered meshes. (English) Zbl 1225.76219 Appl. Numer. Math. 58, No. 7, 1042-1060 (2008). MSC: 76M25 65M06 PDFBibTeX XMLCite \textit{J. Cheng} and \textit{C.-W. Shu}, Appl. Numer. Math. 58, No. 7, 1042--1060 (2008; Zbl 1225.76219) Full Text: DOI
Zhu, Jun; Qiu, Jianxian; Shu, Chi-Wang; Dumbser, Michael Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes. (English) Zbl 1157.65453 J. Comput. Phys. 227, No. 9, 4330-4353 (2008). MSC: 65M60 65M99 35L65 PDFBibTeX XMLCite \textit{J. Zhu} et al., J. Comput. Phys. 227, No. 9, 4330--4353 (2008; Zbl 1157.65453) Full Text: DOI
Shen, Jun; Shu, Chi-Wang; Zhang, Mengping High resolution schemes for a hierarchical size-structured model. (English) Zbl 1144.65059 SIAM J. Numer. Anal. 45, No. 1, 352-370 (2007). Reviewer: Iwan Gawriljuk (Eisenach) MSC: 65M06 65M12 35K55 92D25 PDFBibTeX XMLCite \textit{J. Shen} et al., SIAM J. Numer. Anal. 45, No. 1, 352--370 (2007; Zbl 1144.65059) Full Text: DOI
Chen, Shanqin; E, Weinan; Liu, Yunxian; Shu, Chi-Wang A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations. (English) Zbl 1343.76041 J. Comput. Phys. 225, No. 2, 1314-1330 (2007). MSC: 76M25 76M10 76X05 82C80 65M55 65M60 PDFBibTeX XMLCite \textit{S. Chen} et al., J. Comput. Phys. 225, No. 2, 1314--1330 (2007; Zbl 1343.76041) Full Text: DOI
Xing, Yulong; Shu, Chi-Wang A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. (English) Zbl 1115.65096 Commun. Comput. Phys. 1, No. 1, 100-134 (2006). MSC: 65M06 65M60 35L65 76M12 76M10 76B15 PDFBibTeX XMLCite \textit{Y. Xing} and \textit{C.-W. Shu}, Commun. Comput. Phys. 1, No. 1, 100--134 (2006; Zbl 1115.65096)
Xing, Yulong; Shu, Chi-Wang High-order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms. (English) Zbl 1115.76059 J. Sci. Comput. 27, No. 1-3, 477-494 (2006). MSC: 76M20 65M06 76T10 35L99 PDFBibTeX XMLCite \textit{Y. Xing} and \textit{C.-W. Shu}, J. Sci. Comput. 27, No. 1--3, 477--494 (2006; Zbl 1115.76059) Full Text: DOI
Xing, Yulong; Shu, Chi-Wang High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. (English) Zbl 1089.65091 J. Comput. Phys. 214, No. 2, 567-598 (2006). MSC: 65M06 65M60 35L65 PDFBibTeX XMLCite \textit{Y. Xing} and \textit{C.-W. Shu}, J. Comput. Phys. 214, No. 2, 567--598 (2006; Zbl 1089.65091) Full Text: DOI
Qiu, Jianxian; Khoo, Boo Cheong; Shu, Chi-Wang A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes. (English) Zbl 1083.65093 J. Comput. Phys. 212, No. 2, 540-565 (2006). MSC: 65M60 35L65 PDFBibTeX XMLCite \textit{J. Qiu} et al., J. Comput. Phys. 212, No. 2, 540--565 (2006; Zbl 1083.65093) Full Text: DOI
Xu, Zhengfu; Shu, Chiwang Anti-diffusive high order WENO schemes for Hamilton-Jacobi equations. (English) Zbl 1119.65378 Methods Appl. Anal. 12, No. 2, 169-190 (2005). MSC: 65M06 35L60 49L25 PDFBibTeX XMLCite \textit{Z. Xu} and \textit{C. Shu}, Methods Appl. Anal. 12, No. 2, 169--190 (2005; Zbl 1119.65378) Full Text: DOI
Qiu, Jianxian; Dumbser, Michael; Shu, Chi-Wang The discontinuous Galerkin method with Lax–Wendroff type time discretizations. (English) Zbl 1093.76038 Comput. Methods Appl. Mech. Eng. 194, No. 42-44, 4528-4543 (2005). MSC: 76M10 76N15 PDFBibTeX XMLCite \textit{J. Qiu} et al., Comput. Methods Appl. Mech. Eng. 194, No. 42--44, 4528--4543 (2005; Zbl 1093.76038) Full Text: DOI
Qiu, Jianxian; Shu, Chi-Wang A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters. (English) Zbl 1092.65084 SIAM J. Sci. Comput. 27, No. 3, 995-1013 (2005). MSC: 65M60 35L65 65M06 PDFBibTeX XMLCite \textit{J. Qiu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 27, No. 3, 995--1013 (2005; Zbl 1092.65084) Full Text: DOI
Xing, Yulong; Shu, Chi-Wang High order finite difference WENO schemes with the exact conservation property for the shallow water equations. (English) Zbl 1114.76340 J. Comput. Phys. 208, No. 1, 206-227 (2005). MSC: 76M20 76B15 65M06 PDFBibTeX XMLCite \textit{Y. Xing} and \textit{C.-W. Shu}, J. Comput. Phys. 208, No. 1, 206--227 (2005; Zbl 1114.76340) Full Text: DOI
Xu, Zhengfu; Shu, Chi-Wang Anti-diffusive flux corrections for high order finite difference WENO schemes. (English) Zbl 1087.76080 J. Comput. Phys. 205, No. 2, 458-485 (2005). MSC: 76M20 65M06 PDFBibTeX XMLCite \textit{Z. Xu} and \textit{C.-W. Shu}, J. Comput. Phys. 205, No. 2, 458--485 (2005; Zbl 1087.76080) Full Text: DOI
Qiu, Jianxian; Shu, Chi-Wang Runge-Kutta discontinuous Galerkin method using WENO limiters. (English) Zbl 1077.65109 SIAM J. Sci. Comput. 26, No. 3, 907-929 (2005). MSC: 65M60 65M06 35L65 PDFBibTeX XMLCite \textit{J. Qiu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 26, No. 3, 907--929 (2005; Zbl 1077.65109) Full Text: DOI
Qiu, Jianxian; Shu, Chi-Wang Finite difference WENO schemes with Lax-Wendroff-type time discretizations. (English) Zbl 1034.65073 SIAM J. Sci. Comput. 24, No. 6, 2185-2198 (2003). MSC: 65M06 35L65 76N15 76M20 PDFBibTeX XMLCite \textit{J. Qiu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 24, No. 6, 2185--2198 (2003; Zbl 1034.65073) Full Text: DOI
Zhang, Yong-Tao; Shu, Chi-Wang High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes. (English) Zbl 1034.65051 SIAM J. Sci. Comput. 24, No. 3, 1005-1030 (2003). MSC: 65K10 65M06 65M12 35L60 49J20 49L25 65M50 PDFBibTeX XMLCite \textit{Y.-T. Zhang} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 24, No. 3, 1005--1030 (2003; Zbl 1034.65051) Full Text: DOI
Shi, Jing; Zhang, Yong-Tao; Shu, Chi-Wang Resolution of high order WENO schemes for complicated flow structures. (English) Zbl 1047.76081 J. Comput. Phys. 186, No. 2, 690-696 (2003). MSC: 76M20 76L05 76E17 PDFBibTeX XMLCite \textit{J. Shi} et al., J. Comput. Phys. 186, No. 2, 690--696 (2003; Zbl 1047.76081) Full Text: DOI
Carrillo, José A.; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods. (English) Zbl 1034.82063 J. Comput. Phys. 184, No. 2, 498-525 (2003). MSC: 82D37 82-08 82C40 76P05 76M20 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., J. Comput. Phys. 184, No. 2, 498--525 (2003; Zbl 1034.82063) Full Text: DOI
Qiu, Jianxian; Shu, Chi-Wang On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes. (English) Zbl 1018.65106 J. Comput. Phys. 183, No. 1, 187-209 (2002). MSC: 65M06 65Y20 35L65 35L67 PDFBibTeX XMLCite \textit{J. Qiu} and \textit{C.-W. Shu}, J. Comput. Phys. 183, No. 1, 187--209 (2002; Zbl 1018.65106) Full Text: DOI
Shi, Jing; Hu, Changqing; Shu, Chi-Wang A technique of treating negative weights in WENO schemes. (English) Zbl 0992.65094 J. Comput. Phys. 175, No. 1, 108-127 (2002). MSC: 65M06 65M12 35L65 PDFBibTeX XMLCite \textit{J. Shi} et al., J. Comput. Phys. 175, No. 1, 108--127 (2002; Zbl 0992.65094) Full Text: DOI Link
Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan Strong stability-preserving high-order time discretization methods. (English) Zbl 0967.65098 SIAM Rev. 43, No. 1, 89-112 (2001). Reviewer: Michael Sever (Jerusalem) MSC: 65M12 65M20 65-02 65L06 35L65 PDFBibTeX XMLCite \textit{S. Gottlieb} et al., SIAM Rev. 43, No. 1, 89--112 (2001; Zbl 0967.65098) Full Text: DOI
Carrillo, Jose A.; Gamba, Irene M.; Shu, Chi-Wang Computational macroscopic approximations to the one-dimensional relaxation-time kinetic system for semiconductors. (English) Zbl 0976.82053 Physica D 146, No. 1-4, 289-306 (2000). MSC: 82D37 82C40 35Q99 76P05 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Physica D 146, No. 1--4, 289--306 (2000; Zbl 0976.82053) Full Text: DOI
Liu, Jian-Guo; Shu, Chi-Wang A high-order discontinuous Galerkin method for 2D incompressible flows. (English) Zbl 0963.76069 J. Comput. Phys. 160, No. 2, 577-596 (2000). MSC: 76M25 76M10 76B99 76D05 PDFBibTeX XMLCite \textit{J.-G. Liu} and \textit{C.-W. Shu}, J. Comput. Phys. 160, No. 2, 577--596 (2000; Zbl 0963.76069) Full Text: DOI Link
Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. (English) Zbl 0966.76080 Comput. Methods Appl. Mech. Eng. 181, No. 4, 381-392 (2000). MSC: 76P05 82D37 PDFBibTeX XMLCite \textit{C. Cercignani} et al., Comput. Methods Appl. Mech. Eng. 181, No. 4, 381--392 (2000; Zbl 0966.76080) Full Text: DOI
Hu, Changqing; Shu, Chi-Wang A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. (English) Zbl 0946.65090 SIAM J. Sci. Comput. 21, No. 2, 666-690 (1999). Reviewer: J.D.P.Donnelly (Oxford) MSC: 65M60 65Y05 35Q58 70H20 37J35 PDFBibTeX XMLCite \textit{C. Hu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 21, No. 2, 666--690 (1999; Zbl 0946.65090) Full Text: DOI
Erlebacher, G.; Hussaini, M. Y.; Shu, C.-W. Interaction of a shock with a longitudinal vortex. (English) Zbl 0889.76033 J. Fluid Mech. 337, 129-153 (1997). MSC: 76L05 76N10 76M20 PDFBibTeX XMLCite \textit{G. Erlebacher} et al., J. Fluid Mech. 337, 129--153 (1997; Zbl 0889.76033) Full Text: DOI
Perthame, Benoit; Shu, Chi-Wang On positivity preserving finite volume schemes for Euler equations. (English) Zbl 0857.76062 Numer. Math. 73, No. 1, 119-130 (1996). MSC: 76M25 76N10 PDFBibTeX XMLCite \textit{B. Perthame} and \textit{C.-W. Shu}, Numer. Math. 73, No. 1, 119--130 (1996; Zbl 0857.76062) Full Text: DOI