Cao, Huihui; Huang, Yunqing; Yi, Nianyu Gradient recovery based a posteriori error estimator for the adaptive direct discontinuous Galerkin method. (English) Zbl 1514.65163 Calcolo 60, No. 1, Paper No. 18, 29 p. (2023). MSC: 65N30 65N50 65K10 65N12 65N15 PDFBibTeX XMLCite \textit{H. Cao} et al., Calcolo 60, No. 1, Paper No. 18, 29 p. (2023; Zbl 1514.65163) Full Text: DOI
Cao, Huihui; Huang, Yunqing; Yi, Nianyu Adaptive direct discontinuous Galerkin method for elliptic equations. (English) Zbl 1524.65769 Comput. Math. Appl. 97, 394-415 (2021). MSC: 65N30 65N15 35J25 65N12 PDFBibTeX XMLCite \textit{H. Cao} et al., Comput. Math. Appl. 97, 394--415 (2021; Zbl 1524.65769) Full Text: DOI
Amanbek, Yerlan; Singh, Gurpreet; Pencheva, Gergina; Wheeler, Mary F. Error indicators for incompressible Darcy flow problems using enhanced velocity mixed finite element method. (English) Zbl 1437.76019 Comput. Methods Appl. Mech. Eng. 363, Article ID 112884, 22 p. (2020). MSC: 76M10 65N30 76S05 65N15 PDFBibTeX XMLCite \textit{Y. Amanbek} et al., Comput. Methods Appl. Mech. Eng. 363, Article ID 112884, 22 p. (2020; Zbl 1437.76019) Full Text: DOI arXiv
Dedner, Andreas; Kane, Birane; Klöfkorn, Robert; Nolte, Martin Python framework for \(hp\)-adaptive discontinuous Galerkin methods for two-phase flow in porous media. (English) Zbl 1481.65180 Appl. Math. Modelling 67, 179-200 (2019). MSC: 65M60 76S05 76T10 PDFBibTeX XMLCite \textit{A. Dedner} et al., Appl. Math. Modelling 67, 179--200 (2019; Zbl 1481.65180) Full Text: DOI arXiv Link
Kou, Jisheng; Sun, Shuyu Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state. (English) Zbl 1440.76096 Comput. Methods Appl. Mech. Eng. 341, 221-248 (2018). MSC: 76M12 65M08 49S05 76T10 PDFBibTeX XMLCite \textit{J. Kou} and \textit{S. Sun}, Comput. Methods Appl. Mech. Eng. 341, 221--248 (2018; Zbl 1440.76096) Full Text: DOI arXiv Link
Kou, Jisheng; Sun, Shuyu Thermodynamically consistent modeling and simulation of multi-component two-phase flow with partial miscibility. (English) Zbl 1439.76079 Comput. Methods Appl. Mech. Eng. 331, 623-649 (2018). MSC: 76M10 76S05 65N12 49S05 76T10 PDFBibTeX XMLCite \textit{J. Kou} and \textit{S. Sun}, Comput. Methods Appl. Mech. Eng. 331, 623--649 (2018; Zbl 1439.76079) Full Text: DOI arXiv Link
Yang, Haijian; Sun, Shuyu; Li, Yiteng; Yang, Chao A scalable fully implicit framework for reservoir simulation on parallel computers. (English) Zbl 1439.76103 Comput. Methods Appl. Mech. Eng. 330, 334-350 (2018). MSC: 76M10 65M22 65M60 65Y05 76-10 76S05 76T10 PDFBibTeX XMLCite \textit{H. Yang} et al., Comput. Methods Appl. Mech. Eng. 330, 334--350 (2018; Zbl 1439.76103) Full Text: DOI Link
Kou, Jisheng; Sun, Shuyu Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of state. (English) Zbl 1415.76644 J. Comput. Phys. 371, 581-605 (2018). MSC: 76T10 80A20 76M25 PDFBibTeX XMLCite \textit{J. Kou} and \textit{S. Sun}, J. Comput. Phys. 371, 581--605 (2018; Zbl 1415.76644) Full Text: DOI arXiv
Kou, Jisheng; Sun, Shuyu; Wang, Xiuhua Linearly decoupled energy-stable numerical methods for multicomponent two-phase compressible flow. (English) Zbl 1404.65226 SIAM J. Numer. Anal. 56, No. 6, 3219-3248 (2018). MSC: 65N12 76T10 49S05 65N06 65N08 PDFBibTeX XMLCite \textit{J. Kou} et al., SIAM J. Numer. Anal. 56, No. 6, 3219--3248 (2018; Zbl 1404.65226) Full Text: DOI arXiv
Lee, Sanghyun; Wheeler, Mary F. Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization. (English) Zbl 1378.76048 J. Comput. Phys. 331, 19-37 (2017). MSC: 76M10 65M60 76S05 PDFBibTeX XMLCite \textit{S. Lee} and \textit{M. F. Wheeler}, J. Comput. Phys. 331, 19--37 (2017; Zbl 1378.76048) Full Text: DOI arXiv
Chen, Huangxin; Sun, Shuyu A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media. (English) Zbl 1397.76062 Numer. Math. 136, No. 3, 805-839 (2017). MSC: 76M10 65N30 65N12 65N15 76S05 PDFBibTeX XMLCite \textit{H. Chen} and \textit{S. Sun}, Numer. Math. 136, No. 3, 805--839 (2017; Zbl 1397.76062) Full Text: DOI
Xiong, Chunguang; Becker, Roland; Luo, Fusheng; Ma, Xiuling A priori and a posteriori error analysis for the mixed discontinuous Galerkin finite element approximations of the biharmonic problems. (English) Zbl 1365.65239 Numer. Methods Partial Differ. Equations 33, No. 1, 318-353 (2017). Reviewer: I. N. Katz (St. Louis) MSC: 65N15 65N30 35J40 65N12 PDFBibTeX XMLCite \textit{C. Xiong} et al., Numer. Methods Partial Differ. Equations 33, No. 1, 318--353 (2017; Zbl 1365.65239) Full Text: DOI
Moortgat, Joachim; Firoozabadi, Abbas Mixed-hybrid and vertex-discontinuous-Galerkin finite element modeling of multiphase compositional flow on 3D unstructured grids. (English) Zbl 1349.76241 J. Comput. Phys. 315, 476-500 (2016). MSC: 76M10 65M60 76S05 76Txx PDFBibTeX XMLCite \textit{J. Moortgat} and \textit{A. Firoozabadi}, J. Comput. Phys. 315, 476--500 (2016; Zbl 1349.76241) Full Text: DOI arXiv
Li, Jichun; Lin, Yanping A priori and posteriori error analysis for time-dependent Maxwell’s equations. (English) Zbl 1423.78020 Comput. Methods Appl. Mech. Eng. 292, 54-68 (2015). MSC: 78M10 65M60 35Q61 65M15 PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. Lin}, Comput. Methods Appl. Mech. Eng. 292, 54--68 (2015; Zbl 1423.78020) Full Text: DOI
Zhang, Shuhua; Sun, Shuyu; Yang, Hongtao Optimal convergence of discontinuous Galerkin methods for continuum modeling of supply chain networks. (English) Zbl 1361.35110 Comput. Math. Appl. 68, No. 6, 681-691 (2014). MSC: 35L65 65M60 35L02 65M12 65M15 PDFBibTeX XMLCite \textit{S. Zhang} et al., Comput. Math. Appl. 68, No. 6, 681--691 (2014; Zbl 1361.35110) Full Text: DOI
Karasözen, Bülent; Uzunca, Murat Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism. (English) Zbl 1312.65163 GEM. Int. J. Geomath. 5, No. 2, 255-288 (2014). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M60 65M50 65M15 35K57 PDFBibTeX XMLCite \textit{B. Karasözen} and \textit{M. Uzunca}, GEM. Int. J. Geomath. 5, No. 2, 255--288 (2014; Zbl 1312.65163) Full Text: DOI arXiv
Yang, Jiming; Chen, Yanping A posteriori error analysis for a fully discrete discontinuous Galerkin approximation to a kind of reactive transport problems. (English) Zbl 1307.65121 J. Syst. Sci. Complex. 25, No. 2, 398-409 (2012). MSC: 65M15 65M60 35K20 PDFBibTeX XMLCite \textit{J. Yang} and \textit{Y. Chen}, J. Syst. Sci. Complex. 25, No. 2, 398--409 (2012; Zbl 1307.65121) Full Text: DOI
Feistauer, Miloslav; Sändig, Anna-Margarete Graded mesh refinement and error estimates of higher order for DGFE solutions of elliptic boundary value problems in polygons. (English) Zbl 1253.65193 Numer. Methods Partial Differ. Equations 28, No. 4, 1124-1151 (2012). Reviewer: Nina Shokina (Freiburg) MSC: 65N50 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{M. Feistauer} and \textit{A.-M. Sändig}, Numer. Methods Partial Differ. Equations 28, No. 4, 1124--1151 (2012; Zbl 1253.65193) Full Text: DOI
Yang, Jiming A posteriori error of a discontinuous Galerkin scheme for compressible miscible displacement problems with molecular diffusion and dispersion. (English) Zbl 1428.76178 Int. J. Numer. Methods Fluids 65, No. 7, 781-797 (2011). MSC: 76M99 65M60 65M15 76S05 PDFBibTeX XMLCite \textit{J. Yang}, Int. J. Numer. Methods Fluids 65, No. 7, 781--797 (2011; Zbl 1428.76178) Full Text: DOI
Feistauer, Miloslav; Kučera, Václav; Najzar, Karel; Prokopová, Jaroslava Analysis of space-time discontinuous Galerkin method for nonlinear convection-diffusion problems. (English) Zbl 1211.65125 Numer. Math. 117, No. 2, 251-288 (2011). Reviewer: H. P. Dikshit (Bhopal) MSC: 65M60 65M15 35K61 PDFBibTeX XMLCite \textit{M. Feistauer} et al., Numer. Math. 117, No. 2, 251--288 (2011; Zbl 1211.65125) Full Text: DOI
Yang, Jiming; Chen, Yanping A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems. (English) Zbl 1273.76284 Sci. China, Math. 53, No. 10, 2679-2696 (2010). MSC: 76M10 65M60 76N99 76S05 PDFBibTeX XMLCite \textit{J. Yang} and \textit{Y. Chen}, Sci. China, Math. 53, No. 10, 2679--2696 (2010; Zbl 1273.76284) Full Text: DOI
Creusé, Emmanuel; Nicaise, Serge A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods. (English) Zbl 1197.65174 J. Comput. Appl. Math. 234, No. 10, 2903-2915 (2010). Reviewer: Dietrich Braess (Bochum) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{E. Creusé} and \textit{S. Nicaise}, J. Comput. Appl. Math. 234, No. 10, 2903--2915 (2010; Zbl 1197.65174) Full Text: DOI Link
Kučera, Václav Optimal \(L^{\infty}(L^{2})\)-error estimates for the DG method applied to nonlinear convection-diffusion problems with nonlinear diffusion. (English) Zbl 1195.65118 Numer. Funct. Anal. Optim. 31, No. 3, 285-312 (2010). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M15 65M12 35K61 65M20 PDFBibTeX XMLCite \textit{V. Kučera}, Numer. Funct. Anal. Optim. 31, No. 3, 285--312 (2010; Zbl 1195.65118) Full Text: DOI
Tomar, S. K.; Repin, S. I. Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems. (English) Zbl 1163.65077 J. Comput. Appl. Math. 226, No. 2, 358-369 (2009). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N15 65N30 35J25 35R05 PDFBibTeX XMLCite \textit{S. K. Tomar} and \textit{S. I. Repin}, J. Comput. Appl. Math. 226, No. 2, 358--369 (2009; Zbl 1163.65077) Full Text: DOI
Sun, Shuyu; Dong, Ming Continuum modeling of supply chain networks using discontinuous Galerkin methods. (English) Zbl 1159.74317 Comput. Methods Appl. Mech. Eng. 197, No. 13-16, 1204-1218 (2008). MSC: 74A99 74S30 PDFBibTeX XMLCite \textit{S. Sun} and \textit{M. Dong}, Comput. Methods Appl. Mech. Eng. 197, No. 13--16, 1204--1218 (2008; Zbl 1159.74317) Full Text: DOI
Feistauer, Miloslav; Hájek, Jaroslav; Švadlenka, Karel Space-time discontinuous Galerkin method for solving nonstationary convection-diffusion-reaction problems. (English) Zbl 1164.65469 Appl. Math., Praha 52, No. 3, 197-233 (2007). MSC: 65M60 65M15 65M12 35K15 PDFBibTeX XMLCite \textit{M. Feistauer} et al., Appl. Math., Praha 52, No. 3, 197--233 (2007; Zbl 1164.65469) Full Text: DOI EuDML
Sun, Shuyu; Wheeler, Mary F. Local problem-based a posteriori error estimators for discontinuous Galerkin approximations of reactive transport. (English) Zbl 1117.76061 Comput. Geosci. 11, No. 2, 87-101 (2007). MSC: 76S05 65M15 65M60 76M10 76V05 PDFBibTeX XMLCite \textit{S. Sun} and \textit{M. F. Wheeler}, Comput. Geosci. 11, No. 2, 87--101 (2007; Zbl 1117.76061) Full Text: DOI
Sun, Shuyu; Wheeler, M. F. Analysis of discontinuous Galerkin methods for multicomponent reactive transport problems. (English) Zbl 1129.65068 Comput. Math. Appl. 52, No. 5, 637-650 (2006). Reviewer: Weizhong Dai (Ruston) MSC: 65M60 76M10 76S05 76V05 65M15 65M12 35K55 PDFBibTeX XMLCite \textit{S. Sun} and \textit{M. F. Wheeler}, Comput. Math. Appl. 52, No. 5, 637--650 (2006; Zbl 1129.65068) Full Text: DOI
Sun, Shuyu; Wheeler, Mary F. Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport. (English) Zbl 1175.76096 Comput. Methods Appl. Mech. Eng. 195, No. 25-28, 3382-3405 (2006). MSC: 76M10 76V05 76S05 PDFBibTeX XMLCite \textit{S. Sun} and \textit{M. F. Wheeler}, Comput. Methods Appl. Mech. Eng. 195, No. 25--28, 3382--3405 (2006; Zbl 1175.76096) Full Text: DOI
Sun, Shuyu; Wheeler, Mary F. Projections of velocity data for the compatibility with transport. (English) Zbl 1091.76041 Comput. Methods Appl. Mech. Eng. 195, No. 7-8, 653-673 (2006). MSC: 76M10 76S05 65N30 PDFBibTeX XMLCite \textit{S. Sun} and \textit{M. F. Wheeler}, Comput. Methods Appl. Mech. Eng. 195, No. 7--8, 653--673 (2006; Zbl 1091.76041) Full Text: DOI