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𝑝-robust equivalence of global continuous constrained and local discontinuous unconstrained approximation, a 𝑝-stable local commuting projector, and optimal elementwise ℎ𝑝 approximation estimates in 𝐻(^cp)
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New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance and applications to the Stokes’ equations
An hp-Adaptive Strategy Based on Locally Predicted Error Reductions
Patrick Bammer, Andreas Schröder and Thomas P. Wihler Computational Methods in Applied Mathematics 25(4) 777 (2025) https://doi.org/10.1515/cmam-2023-0250
Enhanced and efficient scaled boundary finite elements for mechanical problems under the action of body loads
Karolinne O. Coelho, Philippe R.B. Devloo and Sônia M. Gomes Computer Methods in Applied Mechanics and Engineering 420 116695 (2024) https://doi.org/10.1016/j.cma.2023.116695
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
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
Residual-based a posteriori error estimates for the hp version of the finite element discretization of the elliptic Robin boundary control problem
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
ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
Error estimates for the Scaled Boundary Finite Element Method
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
High order discontinuous Galerkin method for reduced flow models in fractured porous media
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
hp spectral element approximation for integral state constrained optimal control problems governed by harmonic equations
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
Invisibility and indistinguishability in structural damage tomography
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
A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems
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 Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems
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
A hk mortar spectral element method for the p-Laplacian equation
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
Error analysis of the spectral element method with Gauss–Lobatto–Legendre points for the acoustic wave equation in heterogeneous media
$C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints
Susanne C. Brenner, Joscha Gedicke and Li-yeng Sung SIAM Journal on Numerical Analysis 56(3) 1758 (2018) https://doi.org/10.1137/17M1140649
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
Distributed Lagrange Multiplier Functions for Fictitious Domain Method with Spectral/hp Element Discretization
A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem
High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations
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
Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity
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
$hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes
Andrea Cangiani, Zhaonan Dong and Emmanuil H. Georgoulis SIAM Journal on Scientific Computing 39(4) A1251 (2017) https://doi.org/10.1137/16M1073285
A coupled electro-thermal Discontinuous Galerkin method