Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM
ESAIM: M2AN, 48 3 (2014) 727-752
Published online: 2014-02-11
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
Lise-Marie Imbert-Gérard, Andrea Moiola, Chiara Perinati and Paul StockerIMA Journal of Numerical Analysis (2025)
https://doi.org/10.1093/imanum/drae094
Trefftz discontinuous Galerkin discretization for the Stokes problem
Philip L. Lederer, Christoph Lehrenfeld and Paul StockerNumerische Mathematik 156 (3) 979 (2024)
https://doi.org/10.1007/s00211-024-01404-z
The Trefftz methods for 3D biharmonic equation using directors and in-plane biharmonic functions
Chein-Shan Liu and Chung-Lun KuoEngineering with Computers 40 (5) 3337 (2024)
https://doi.org/10.1007/s00366-024-01977-1
Embedded Trefftz discontinuous Galerkin methods
Christoph Lehrenfeld and Paul StockerInternational Journal for Numerical Methods in Engineering 124 (17) 3637 (2023)
https://doi.org/10.1002/nme.7258
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Fabian Heimann, Christoph Lehrenfeld, Paul Stocker and Henry von WahlESAIM: Mathematical Modelling and Numerical Analysis 57 (5) 2803 (2023)
https://doi.org/10.1051/m2an/2023064
p- and hp- virtual elements for the Stokes problem
A. Chernov, C. Marcati and L. MascottoAdvances in Computational Mathematics 47 (2) (2021)
https://doi.org/10.1007/s10444-020-09831-w
Conforming and nonconforming harmonic finite elements
Tatyana Sorokina and Shangyou ZhangApplicable Analysis 99 (4) 569 (2020)
https://doi.org/10.1080/00036811.2018.1504031
Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number
Lorenzo Mascotto and Alexander PichlerApplied Numerical Mathematics 155 160 (2020)
https://doi.org/10.1016/j.apnum.2019.04.005
A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations
Håkon Sem Fure, Sébastien Pernet, Margot Sirdey and Sébastien TordeuxSN Partial Differential Equations and Applications 1 (4) (2020)
https://doi.org/10.1007/s42985-020-00024-0
A new mixed discontinuous Galerkin method for the electrostatic field
Abdelhamid Zaghdani and Mohamed EzzatAdvances in Difference Equations 2019 (1) (2019)
https://doi.org/10.1186/s13662-019-2420-x
A nonconforming Trefftz virtual element method for the Helmholtz problem: Numerical aspects
Lorenzo Mascotto, Ilaria Perugia and Alexander PichlerComputer Methods in Applied Mechanics and Engineering 347 445 (2019)
https://doi.org/10.1016/j.cma.2018.12.039
Solving Laplace Problems with Corner Singularities via Rational Functions
Abinand Gopal and Lloyd N. TrefethenSIAM Journal on Numerical Analysis 57 (5) 2074 (2019)
https://doi.org/10.1137/19M125947X
The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domains
Alexey Chernov and Lorenzo MascottoIMA Journal of Numerical Analysis 39 (4) 1787 (2019)
https://doi.org/10.1093/imanum/dry038
Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions
Marina B. Yuldasheva and Oleg I. YuldashevRussian Journal of Numerical Analysis and Mathematical Modelling 34 (3) 175 (2019)
https://doi.org/10.1515/rnam-2019-0015
An oversampled collocation approach of the Wave Based Method for Helmholtz problems
Daan Huybrechs and Anda-Elena OlteanuWave Motion 87 92 (2019)
https://doi.org/10.1016/j.wavemoti.2018.06.001
Non-conforming Harmonic Virtual Element Method: $$h$$ h - and $$p$$ p -Versions
Lorenzo Mascotto, Ilaria Perugia and Alexander PichlerJournal of Scientific Computing 77 (3) 1874 (2018)
https://doi.org/10.1007/s10915-018-0797-4
Exponential convergence of the hp virtual element method in presence of corner singularities
L. Beirão da Veiga, A. Chernov, L. Mascotto and A. RussoNumerische Mathematik 138 (3) 581 (2018)
https://doi.org/10.1007/s00211-017-0921-7
Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions
Vladimir Kazeev and Christoph SchwabNumerische Mathematik 138 (1) 133 (2018)
https://doi.org/10.1007/s00211-017-0899-1
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
Alice Lieu, Gwénaël Gabard and Hadrien BériotJournal of Computational Physics 321 105 (2016)
https://doi.org/10.1016/j.jcp.2016.05.045
Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the $$hp$$ h p -Version
R. Hiptmair, A. Moiola and I. PerugiaFoundations of Computational Mathematics 16 (3) 637 (2016)
https://doi.org/10.1007/s10208-015-9260-1
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Ralf Hiptmair, Andrea Moiola and Ilaria PerugiaLecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 237 (2016)
https://doi.org/10.1007/978-3-319-41640-3_8