Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H. A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes. (English) Zbl 1526.65052 SIAM J. Numer. Anal. 61, No. 5, 2352-2380 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65J10 65N15 65N12 65N50 65N85 41A25 PDFBibTeX XMLCite \textit{A. Cangiani} et al., SIAM J. Numer. Anal. 61, No. 5, 2352--2380 (2023; Zbl 1526.65052) Full Text: DOI arXiv
Georgoulis, Emmanuil H.; Loulakis, Michail; Tsiourvas, Asterios Discrete gradient flow approximations of high dimensional evolution partial differential equations via deep neural networks. (English) Zbl 07634536 Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106893, 11 p. (2023). MSC: 68Txx 65Mxx 65Cxx PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106893, 11 p. (2023; Zbl 07634536) Full Text: DOI arXiv
Dong, Zhaonan; Georgoulis, Emmanuil H. Robust interior penalty discontinuous Galerkin methods. (English) Zbl 1502.65197 J. Sci. Comput. 92, No. 2, Paper No. 57, 23 p. (2022). MSC: 65N30 65N15 35J70 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{E. H. Georgoulis}, J. Sci. Comput. 92, No. 2, Paper No. 57, 23 p. (2022; Zbl 1502.65197) Full Text: DOI arXiv
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H. \(hp\)-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. (English) Zbl 1484.65295 Math. Comput. 91, No. 333, 1-35 (2022). MSC: 65N30 65N50 65N15 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Math. Comput. 91, No. 333, 1--35 (2022; Zbl 1484.65295) Full Text: DOI arXiv
Cangiani, Andrea; Georgoulis, Emmanuil H.; Sutton, Oliver J. Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods. (English) Zbl 1473.65178 Math. Models Methods Appl. Sci. 31, No. 4, 711-751 (2021). MSC: 65M50 65N15 65N30 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Math. Models Methods Appl. Sci. 31, No. 4, 711--751 (2021; Zbl 1473.65178) Full Text: DOI arXiv
Georgoulis, Emmanuil H.; Lakkis, Omar; Wihler, Thomas P. A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems. (English) Zbl 1486.65168 Numer. Math. 148, No. 2, 363-386 (2021). Reviewer: Dana Černá (Liberec) MSC: 65M60 65N30 65M15 65M50 PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., Numer. Math. 148, No. 2, 363--386 (2021; Zbl 1486.65168) Full Text: DOI arXiv
Chrysafinos, Konstantinos; Georgoulis, Emmanuil H.; Plaka, Dimitra A posteriori error estimates for the Allen-Cahn problem. (English) Zbl 1453.65312 SIAM J. Numer. Anal. 58, No. 5, 2662-2683 (2020). MSC: 65M60 65M06 65N30 65M15 PDFBibTeX XMLCite \textit{K. Chrysafinos} et al., SIAM J. Numer. Anal. 58, No. 5, 2662--2683 (2020; Zbl 1453.65312) Full Text: DOI arXiv
Dong, Zhaonan; Georgoulis, Emmanuil H.; Pryer, Tristan Recovered finite element methods on polygonal and polyhedral meshes. (English) Zbl 1446.65165 ESAIM, Math. Model. Numer. Anal. 54, No. 4, 1309-1337 (2020). MSC: 65N30 65N50 65N55 35B45 PDFBibTeX XMLCite \textit{Z. Dong} et al., ESAIM, Math. Model. Numer. Anal. 54, No. 4, 1309--1337 (2020; Zbl 1446.65165) Full Text: DOI arXiv Link
Cangiani, Andrea; Georgoulis, Emmanuil H.; Sabawi, Mohammad A posteriori error analysis for implicit-explicit hp-discontinuous Galerkin timestepping methods for semilinear parabolic problems. (English) Zbl 1473.65184 J. Sci. Comput. 82, No. 2, Paper No. 26, 24 p. (2020). Reviewer: Konstantinos Chrysafinos (Athens) MSC: 65M60 65M06 65M15 65N30 35K58 PDFBibTeX XMLCite \textit{A. Cangiani} et al., J. Sci. Comput. 82, No. 2, Paper No. 26, 24 p. (2020; Zbl 1473.65184) Full Text: DOI
Cangiani, Andrea; Georgoulis, Emmanuil H.; Sabawi, Younis A. Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems. (English) Zbl 1462.76127 J. Comput. Appl. Math. 367, Article ID 112397, 15 p. (2020). MSC: 76M10 76S05 80A19 PDFBibTeX XMLCite \textit{A. Cangiani} et al., J. Comput. Appl. Math. 367, Article ID 112397, 15 p. (2020; Zbl 1462.76127) Full Text: DOI Link
Cangiani, A.; Georgoulis, E. H.; Giani, Stefano; Metcalfe, S. \(hp\)-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. (English) Zbl 1443.65197 Comput. Math. Appl. 78, No. 9, 3090-3104 (2019). MSC: 65M60 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Comput. Math. Appl. 78, No. 9, 3090--3104 (2019; Zbl 1443.65197) Full Text: DOI
Dong, Zhaonan; Georgoulis, Emmanuil H.; Levesley, Jeremy; Usta, Fuat A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. (English) Zbl 1442.65365 Comput. Math. Appl. 76, No. 8, 1950-1965 (2018). MSC: 65N30 65N75 35R60 PDFBibTeX XMLCite \textit{Z. Dong} et al., Comput. Math. Appl. 76, No. 8, 1950--1965 (2018; Zbl 1442.65365) Full Text: DOI Link
Georgoulis, Emmanuil H.; Pryer, Tristan Recovered finite element methods. (English) Zbl 1440.65202 Comput. Methods Appl. Mech. Eng. 332, 303-324 (2018). MSC: 65N30 PDFBibTeX XMLCite \textit{E. H. Georgoulis} and \textit{T. Pryer}, Comput. Methods Appl. Mech. Eng. 332, 303--324 (2018; Zbl 1440.65202) Full Text: DOI arXiv Link
Cangiani, Andrea; Georgoulis, Emmanuil H.; Sabawi, Younis A. Adaptive discontinuous Galerkin methods for elliptic interface problems. (English) Zbl 1397.65252 Math. Comput. 87, No. 314, 2675-2707 (2018). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Math. Comput. 87, No. 314, 2675--2707 (2018; Zbl 1397.65252) Full Text: DOI Link
Kreuzer, Christian; Georgoulis, Emmanuil H. Convergence of adaptive discontinuous Galerkin methods. (English) Zbl 1412.65219 Math. Comput. 87, No. 314, 2611-2640 (2018); corrigendum ibid. 90, No. 328, 637-640 (2021). Reviewer: Konstantinos Chrysafinos (Athens) MSC: 65N30 65N12 65N50 65N15 PDFBibTeX XMLCite \textit{C. Kreuzer} and \textit{E. H. Georgoulis}, Math. Comput. 87, No. 314, 2611--2640 (2018; Zbl 1412.65219) Full Text: DOI arXiv
Georgoulis, Emmanuil H.; Pryer, Tristan Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data. (English) Zbl 1421.65030 Calcolo 54, No. 4, 1533-1551 (2017). Reviewer: Vit Dolejsi (Praha) MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{E. H. Georgoulis} and \textit{T. Pryer}, Calcolo 54, No. 4, 1533--1551 (2017; Zbl 1421.65030) Full Text: DOI arXiv
Cangiani, Andrea; Georgoulis, Emmanuil H.; Pryer, Tristan; Sutton, Oliver J. A posteriori error estimates for the virtual element method. (English) Zbl 1384.65079 Numer. Math. 137, No. 4, 857-893 (2017). Reviewer: Sarah Eberle (Tübingen) MSC: 65N15 65N30 65N12 35J25 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Numer. Math. 137, No. 4, 857--893 (2017; Zbl 1384.65079) Full Text: DOI arXiv Link
Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H. \(hp\)-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. (English) Zbl 1371.65106 SIAM J. Sci. Comput. 39, No. 4, A1251-A1279 (2017). MSC: 65M60 35K90 65J08 65M50 65M15 PDFBibTeX XMLCite \textit{A. Cangiani} et al., SIAM J. Sci. Comput. 39, No. 4, A1251--A1279 (2017; Zbl 1371.65106) Full Text: DOI arXiv
Banjai, Lehel; Georgoulis, Emmanuil H.; Lijoka, Oluwaseun A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation. (English) Zbl 1355.65130 SIAM J. Numer. Anal. 55, No. 1, 63-86 (2017). MSC: 65M60 35L05 65M12 PDFBibTeX XMLCite \textit{L. Banjai} et al., SIAM J. Numer. Anal. 55, No. 1, 63--86 (2017; Zbl 1355.65130) Full Text: DOI arXiv
Antonietti, Paola F.; Cangiani, Andrea; Collis, Joe; Dong, Zhaonan; Georgoulis, Emmanuil H.; Giani, Stefano; Houston, Paul Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. (English) Zbl 1357.65251 Barrenechea, Gabriel R. (ed.) et al., Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Selected papers based on the presentations at the 101st LMS-EPSRC symposium, Durham, UK, July 8–16, 2014. Cham: Springer (ISBN 978-3-319-41638-0/hbk; 978-3-319-41640-3/ebook). Lecture Notes in Computational Science and Engineering 114, 281-310 (2016). MSC: 65N30 65N50 65M60 65M50 35J25 35L04 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Lect. Notes Comput. Sci. Eng. 114, 281--310 (2016; Zbl 1357.65251) Full Text: DOI Link
Cangiani, Andrea; Georgoulis, Emmanuil H.; Kyza, Irene; Metcalfe, Stephen Adaptivity and blow-up detection for nonlinear evolution problems. (English) Zbl 1355.65118 SIAM J. Sci. Comput. 38, No. 6, A3833-A3856 (2016). MSC: 65M15 35K58 65M50 65M60 35B44 PDFBibTeX XMLCite \textit{A. Cangiani} et al., SIAM J. Sci. Comput. 38, No. 6, A3833--A3856 (2016; Zbl 1355.65118) Full Text: DOI arXiv
Cangiani, Andrea; Georgoulis, Emmanuil H.; Jensen, Max Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes. (English) Zbl 1336.65162 Appl. Numer. Math. 104, 3-14 (2016). MSC: 65M60 35K58 80A20 35K57 65M15 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Appl. Numer. Math. 104, 3--14 (2016; Zbl 1336.65162) Full Text: DOI Link
Georgoulis, Emmanuil H.; Lakkis, Omar; Makridakis, Charalambos G.; Virtanen, Juha M. A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. (English) Zbl 1331.65129 SIAM J. Numer. Anal. 54, No. 1, 120-136 (2016). MSC: 65M15 35L05 65M06 PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., SIAM J. Numer. Anal. 54, No. 1, 120--136 (2016; Zbl 1331.65129) Full Text: DOI arXiv Link
Georgoulis, Emmanuil H.; Virtanen, Juha M. Adaptive discontinuous Galerkin approximations to fourth order parabolic problems. (English) Zbl 1319.65088 Math. Comput. 84, No. 295, 2163-2190 (2015). MSC: 65M20 65M06 65M60 35K35 65M15 PDFBibTeX XMLCite \textit{E. H. Georgoulis} and \textit{J. M. Virtanen}, Math. Comput. 84, No. 295, 2163--2190 (2015; Zbl 1319.65088) Full Text: DOI arXiv
Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. (English) Zbl 1298.65167 Math. Models Methods Appl. Sci. 24, No. 10, 2009-2041 (2014). Reviewer: Constantin Popa (Constanţa) MSC: 65N30 65N50 65N55 35J05 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Math. Models Methods Appl. Sci. 24, No. 10, 2009--2041 (2014; Zbl 1298.65167) Full Text: DOI
Georgoulis, Emmanuil H.; Hall, Edward; Makridakis, Charalambos Error control for discontinuous Galerkin methods for first-order hyperbolic problems. (English) Zbl 1282.65110 Feng, Xiaobing (ed.) et al., Recent developments in discontinuous Galerkin finite element methods for partial differential equations. Papers based on the 2012 John H. Barrett memorial lectures, Knoxville, TN, USA, May 9–11, 2012. Cham: Springer (ISBN 978-3-319-01817-1/hbk; 978-3-319-01818-8/ebook). The IMA Volumes in Mathematics and its Applications 157, 195-207 (2014). MSC: 65M15 65M60 35L02 PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., IMA Vol. Math. Appl. 157, 195--207 (2014; Zbl 1282.65110) Full Text: DOI
Georgoulis, Emmanuil H. Discontinuous Galerkin methods for linear problems: an introduction. (English) Zbl 1250.65139 Georgoulis, Emmanuil H. (ed.) et al., Approximation algorithms for complex systems. Proceedings of the 6th international conference on algorithms for approximation, Ambleside, UK, August 31st – September 4th, 2009. Berlin: Springer (ISBN 978-3-642-16875-8/hbk; 978-3-642-16876-5/ebook). Springer Proceedings in Mathematics 3, 91-126 (2011). MSC: 65N30 35J05 35J25 65N08 65N15 PDFBibTeX XMLCite \textit{E. H. Georgoulis}, Springer Proc. Math. 3, 91--126 (2011; Zbl 1250.65139) Full Text: DOI
Georgoulis, Emmanuil H.; Hall, Edward; Melenk, Jens Markus On the suboptimality of the \(p\)-version interior penalty discontinuous Galerkin method. (English) Zbl 1203.65253 J. Sci. Comput. 42, No. 1, 54-67 (2010). MSC: 65N30 PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., J. Sci. Comput. 42, No. 1, 54--67 (2010; Zbl 1203.65253) Full Text: DOI
Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. II: A posteriori error analysis and adaptivity. (English) Zbl 1175.65127 Appl. Numer. Math. 59, No. 9, 2179-2194 (2009). MSC: 65N15 65N30 65N50 35J25 PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., Appl. Numer. Math. 59, No. 9, 2179--2194 (2009; Zbl 1175.65127) Full Text: DOI
Georgoulis, Emmanuil H. Inverse-type estimates on \(hp\)-finite element spaces and applications. (English) Zbl 1130.65063 Math. Comput. 77, No. 261, 201-219 (2008). Reviewer: Iulian Coroian (Baia Mare) MSC: 65J05 65R20 65N30 65N38 PDFBibTeX XMLCite \textit{E. H. Georgoulis}, Math. Comput. 77, No. 261, 201--219 (2008; Zbl 1130.65063) Full Text: DOI