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hp-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes
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Automatic Mesh Refinement Process for High-Quality Factor Resonant Cavities Using the Method of Moments
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A stable local commuting projector and optimal hp approximation estimates in $$\varvec{H}(\textrm{curl})$$
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Paul Houston, Matthew E. Hubbard, Thomas J. Radley, Oliver J. Sutton and Richard S. J. Widdowson Journal of Scientific Computing 100(2) (2024) https://doi.org/10.1007/s10915-024-02569-3
Analysis of a full-discrete two-grid discontinuous Galerkin method for nonlinear parabolic equations
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in
H
(div)
Alexandre Ern, Thirupathi Gudi, Iain Smears and Martin Vohralík IMA Journal of Numerical Analysis 42(2) 1023 (2022) https://doi.org/10.1093/imanum/draa103
An MsFEM Approach Enriched Using Legendre Polynomials
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Formulation of 3D finite elements using curvilinear coordinates
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Karolinne O. Coelho, Philippe R.B. Devloo and Sônia M. Gomes Computer Methods in Applied Mechanics and Engineering 379 113765 (2021) https://doi.org/10.1016/j.cma.2021.113765
Enrichment of the nonconforming virtual element method with singular functions
A unified algorithm for the selection of collocation stencils for convex, concave, and singular problems
Thibault Jacquemin and Stéphane P. A. Bordas International Journal for Numerical Methods in Engineering 122(16) 4292 (2021) https://doi.org/10.1002/nme.6703
High order discontinuous Galerkin method for reduced flow models in fractured porous media
A high-order discontinuous Galerkin method for nonlinear sound waves
Paola F. Antonietti, Ilario Mazzieri, Markus Muhr, Vanja Nikolić and Barbara Wohlmuth Journal of Computational Physics 415 109484 (2020) https://doi.org/10.1016/j.jcp.2020.109484
Convergence analysis of an energy based discontinuous Galerkin method for the wave equation in second-order form: hp version
Априорные оценки локального разрывного метода Галеркина на разнесенных сетках
для решения уравнения параболического типа в рамках однородной задачи Дирихле
Ruslan V. Zhalnin, Руслан Викторович Жалнин, Виктор Федорович Масягин, et al. Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 24(1) 116 (2020) https://doi.org/10.14498/vsgtu1747
Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids
Paola F. Antonietti, Chiara Facciolà, Alessandro Russo and Marco Verani SIAM Journal on Scientific Computing 41(1) A109 (2019) https://doi.org/10.1137/17M1138194
A lowest-order weak Galerkin method for linear elasticity
Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II
Philip L. Lederer, Christoph Lehrenfeld and Joachim Schöberl ESAIM: Mathematical Modelling and Numerical Analysis 53(2) 503 (2019) https://doi.org/10.1051/m2an/2018054
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Ali Vaziri Astaneh, Federico Fuentes, Jaime Mora and Leszek Demkowicz Computer Methods in Applied Mechanics and Engineering 332 686 (2018) https://doi.org/10.1016/j.cma.2017.12.011
Exponential convergence of the hp virtual element method in presence of corner singularities
Joachim Gwinner and Ernst Peter Stephan Springer Series in Computational Mathematics, Advanced Boundary Element Methods 52 223 (2018) https://doi.org/10.1007/978-3-319-92001-6_7
Predictor–corrector p- and hp-versions of the finite element method for Poisson’s equation in polygonal domains
Galerkin Method with Discontinuous Basis Functions on Staggered Grips a Priory Estimates for the Homogeneous Dirichlet Problem
R.V. Zhalnin and V.F. Masyagin Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 11(2) 29 (2018) https://doi.org/10.14529/mmp180203
Polynomial robust stability analysis for $H$(div)-conforming finite elements for the Stokes equations
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A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics
Paola F Antonietti, Ilario Mazzieri, Niccolò Dal Santo and Alfio Quarteroni IMA Journal of Numerical Analysis 38(4) 1709 (2018) https://doi.org/10.1093/imanum/drx062
A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations
An hp-Hybrid High-Order Method for Variable Diffusion on General Meshes
Joubine Aghili, Daniele A. Di Pietro and Berardo Ruffini Computational Methods in Applied Mathematics 17(3) 359 (2017) https://doi.org/10.1515/cmam-2017-0009
A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation
Lehel Banjai, Emmanuil H. Georgoulis and Oluwaseun Lijoka SIAM Journal on Numerical Analysis 55(1) 63 (2017) https://doi.org/10.1137/16M1065744
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis and Paul Houston SpringerBriefs in Mathematics, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes 23 (2017) https://doi.org/10.1007/978-3-319-67673-9_3
Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016
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Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects