Optimal convergence rates in <i>L</i><sup>2</sup> for a first order system least squares finite element method-Reference-Cited by-同舟云学术

Optimal convergence rates in L² for a first order system least squares finite element method

Published:2023-01 Issue:1 Volume:57 Page:107-141
ISSN:2822-7840
Container-title:ESAIM: Mathematical Modelling and Numerical Analysis
language:
Short-container-title:ESAIM: M2AN

Author:

Bernkopf Maximilian,Melenk Jens Markus

Abstract

We analyze a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. We prove optimal convergence in the L2(Ω) norm for the scalar variable. Numerical results confirm our findings.

Funder

Austrian Science Fund

Publisher

EDP Sciences

Link

https://www.esaim-m2an.org/10.1051/m2an/2022026/pdf

Reference24 articles.

1. Regularity estimates for elliptic boundary value problems in Besov spaces

2. Bernkopf M. and Melenk J.M., Analysis of the hp-version of a first order system least squares method for the Helmholtz equation, in Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, edited by Apel T., Langer U., Meyer A. and Steinbach O.. Springer International Publishing, Cham (2019) 57–84.

3. Bernkopf M. and Melenk J.M., Optimal convergence rates in L2 for a first order system least squares finite element method. Part I: homogeneous boundary conditions. Preprint https://arxiv.org/abs/2012.12919 (2020).

4. On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles

5. Bochev P.B. and Gunzburger M.D., Least-Squares Finite Element Methods. Vol. 166 of Applied Mathematical Sciences. Springer, New York (2009).

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