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Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
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A parameter-free and locking-free enriched Galerkin method of arbitrary order for linear elasticity
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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 simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem
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
A stable space-time FE method for the shallow water equations
A stable mixed finite element method for nearly incompressible linear elastostatics
Eirik Valseth, Albert Romkes, Austin R. Kaul and Clint Dawson International Journal for Numerical Methods in Engineering 122(17) 4709 (2021) https://doi.org/10.1002/nme.6743
Quantum algorithms for escaping from saddle points
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
A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations
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
Enrichment of the nonconforming virtual element method with singular functions
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
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
Asymptotics of the generalized Gegenbauer functions of fractional degree
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 lowest-order weak Galerkin method for linear elasticity
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
A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem
$C^0$ 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
Exponential convergence of the hp virtual element method in presence of corner singularities
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
Advanced Boundary Element Methods
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
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
Distributed Lagrange Multiplier Functions for Fictitious Domain Method with Spectral/hp Element Discretization
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016
Paola F. Antonietti, Alberto Ferroni, Ilario Mazzieri and Alfio Quarteroni Lecture Notes in Computational Science and Engineering, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 119 3 (2017) https://doi.org/10.1007/978-3-319-65870-4_1
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
A coupled electro-thermal Discontinuous Galerkin method
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
Numerical simulation of resistivity LWD tool based on higher-order vector finite element
Basic principles of hp virtual elements on quasiuniform meshes
L. Beir ao da Veiga, A. Chernov, L. Mascotto and A. Russo Mathematical Models and Methods in Applied Sciences 26(08) 1567 (2016) https://doi.org/10.1142/S021820251650038X
Construction and Analysis of HDG Methods for Linearized Shallow Water Equations