Wu, Kailiang; Shu, Chi-Wang Geometric quasilinearization framework for analysis and design of bound-preserving schemes. (English) Zbl 1527.65082 SIAM Rev. 65, No. 4, 1031-1073 (2023). MSC: 65M08 65M06 65N08 65M12 35L65 35Q31 35Q35 76N10 76N15 76M12 76M20 PDFBibTeX XMLCite \textit{K. Wu} and \textit{C.-W. Shu}, SIAM Rev. 65, No. 4, 1031--1073 (2023; Zbl 1527.65082) Full Text: DOI arXiv
Wu, Kailiang; Jiang, Haili; Shu, Chi-Wang Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations. (English) Zbl 1516.65102 SIAM J. Numer. Anal. 61, No. 1, 250-285 (2023). Reviewer: Shuji Yoshikawa (Oita) MSC: 65M60 65M06 65N30 65M12 76W05 76N10 35L65 PDFBibTeX XMLCite \textit{K. Wu} et al., SIAM J. Numer. Anal. 61, No. 1, 250--285 (2023; Zbl 1516.65102) Full Text: DOI arXiv
Xu, Ziyao; Shu, Chi-Wang Third order maximum-principle-satisfying and positivity-preserving Lax-Wendroff discontinuous Galerkin methods for hyperbolic conservation laws. (English) Zbl 07599623 J. Comput. Phys. 470, Article ID 111591, 52 p. (2022). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{Z. Xu} and \textit{C.-W. Shu}, J. Comput. Phys. 470, Article ID 111591, 52 p. (2022; Zbl 07599623) Full Text: DOI
Wu, Kailiang; Shu, Chi-Wang Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations. (English) Zbl 1480.65271 Numer. Math. 148, No. 3, 699-741 (2021). MSC: 65M60 65M06 65N30 65M12 35L65 76W05 76Y05 76M10 PDFBibTeX XMLCite \textit{K. Wu} and \textit{C.-W. Shu}, Numer. Math. 148, No. 3, 699--741 (2021; Zbl 1480.65271) Full Text: DOI arXiv
Liu, Yong; Liu, Qingyuan; Liu, Yuan; Shu, Chi-Wang; Zhang, Mengping Locally divergence-free spectral-DG methods for ideal magnetohydrodynamic equations on cylindrical coordinates. (English) Zbl 1473.65208 Commun. Comput. Phys. 26, No. 3, 631-653 (2019). MSC: 65M60 65M70 76W05 PDFBibTeX XMLCite \textit{Y. Liu} et al., Commun. Comput. Phys. 26, No. 3, 631--653 (2019; Zbl 1473.65208) 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
Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes. (English) Zbl 1411.76111 Comput. Fluids 183, 53-65 (2019). MSC: 76M20 65M06 PDFBibTeX XMLCite \textit{F. Zheng} et al., Comput. Fluids 183, 53--65 (2019; Zbl 1411.76111) 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
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 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