Analysis of non-conforming DPG methods on polyhedral meshes using fractional Sobolev norms

Bacuta, Constantin; Demkowicz, Leszek; Mora, Jaime; Xenophontos, Christos

doi:10.1016/j.camwa.2020.09.018

Title: Analysis of non-conforming DPG methods on polyhedral meshes using fractional Sobolev norms

Journal Article · 01 August 2021 · Computers and Mathematics with Applications (Oxford)

DOI: https://doi.org/10.1016/j.camwa.2020.09.018 · OSTI ID:1809639

Bacuta, Constantin; Demkowicz, Leszek; Mora, Jaime; Xenophontos, Christos

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Sponsoring Organization:: USDOE

OSTI ID:: 1809639

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Journal Issue: C Vol. 95; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (16)

Using finite element tools in proving shift theorems for elliptic boundary value problems Bacuta, Constantin; H. Bramble, James; E. Pasciak, Joseph Numerical Linear Algebra with Applications, Vol. 10, Issue 1-2 https://doi.org/10.1002/nla.311	journal	January 2002
Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons Mousavi, S. E.; Sukumar, N. Computational Mechanics, Vol. 47, Issue 5 https://doi.org/10.1007/s00466-010-0562-5	journal	December 2010
Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra Chin, Eric B.; Lasserre, Jean B.; Sukumar, N. Computational Mechanics, Vol. 56, Issue 6 https://doi.org/10.1007/s00466-015-1213-7	journal	October 2015
De Rham diagram for hp finite element spaces Demkowicz, L.; Monk, P.; Vardapetyan, L. Computers & Mathematics with Applications, Vol. 39, Issue 7-8 https://doi.org/10.1016/S0898-1221(00)00062-6	journal	April 2000
Hitchhikerʼs guide to the fractional Sobolev spaces Di Nezza, Eleonora; Palatucci, Giampiero; Valdinoci, Enrico Bulletin des Sciences Mathématiques, Vol. 136, Issue 5 https://doi.org/10.1016/j.bulsci.2011.12.004	journal	July 2012
Note on discontinuous trace approximation in the practical DPG method Heuer, Norbert; Karkulik, Michael; Sayas, Francisco-Javier Computers & Mathematics with Applications, Vol. 68, Issue 11 https://doi.org/10.1016/j.camwa.2014.07.006	journal	December 2014
Orientation embedded high order shape functions for the exact sequence elements of all shapes Fuentes, Federico; Keith, Brendan; Demkowicz, Leszek Computers & Mathematics with Applications, Vol. 70, Issue 4 https://doi.org/10.1016/j.camwa.2015.04.027	journal	August 2015
Breaking spaces and forms for the DPG method and applications including Maxwell equations Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. Computers & Mathematics with Applications, Vol. 72, Issue 3 https://doi.org/10.1016/j.camwa.2016.05.004	journal	August 2016
A class of discontinuous Petrov–Galerkin methods. Part I: The transport equation Demkowicz, L.; Gopalakrishnan, J. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 23-24 https://doi.org/10.1016/j.cma.2010.01.003	journal	April 2010
High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime Computer Methods in Applied Mechanics and Engineering, Vol. 332 https://doi.org/10.1016/j.cma.2017.12.011	journal	April 2018
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations Bassi, F.; Botti, L.; Colombo, A. Journal of Computational Physics, Vol. 231, Issue 1 https://doi.org/10.1016/j.jcp.2011.08.018	journal	January 2012
Regularity estimates for elliptic boundary value problems in Besov spaces Bacuta, Constantin; Bramble, James H.; Xu, Jinchao Mathematics of Computation, Vol. 72, Issue 244 https://doi.org/10.1090/S0025-5718-02-01502-8	journal	December 2002
Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples Chandler-Wilde, S. N.; Hewett, D. P.; Moiola, A. Mathematika, Vol. 61, Issue 2 https://doi.org/10.1112/S0025579314000278	journal	November 2014
Analysis of the DPG Method for the Poisson Equation Demkowicz, L.; Gopalakrishnan, J. SIAM Journal on Numerical Analysis, Vol. 49, Issue 5 https://doi.org/10.1137/100809799	journal	January 2011
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs Karypis, George; Kumar, Vipin SIAM Journal on Scientific Computing, Vol. 20, Issue 1 https://doi.org/10.1137/S1064827595287997	journal	January 1998
The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach Spaces Muga, Ignacio; Tyler, Matthew J. W.; van der Zee, Kristoffer G. Computational Methods in Applied Mathematics, Vol. 19, Issue 3 https://doi.org/10.1515/cmam-2018-0199	journal	July 2019

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