Optimal convergence rates in $L^2$ for a first order system least squares finite element method. Part I: homogeneous boundary conditions

Maximilian Bernkopf; Jens Markus Melenk

doi:10.1051/m2an/2022026

Optimal convergence rates in $L^2$ for a first order system least squares finite element method. Part I: homogeneous boundary conditions

Numerical Analysis 2024-07-25 v1 Numerical Analysis

Authors: Maximilian Bernkopf , Jens Markus Melenk

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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 $L^2(\Omega)$ norm for the scalar variable. Numerical results confirm our findings.

Keywords

first order system least squares finite element method elliptic problem homogeneous boundary conditions optimal convergence l2 norm

Cite

@article{arxiv.2012.12919,
  title  = {Optimal convergence rates in $L^2$ for a first order system least squares finite element method. Part I: homogeneous boundary conditions},
  author = {Maximilian Bernkopf and Jens Markus Melenk},
  journal= {arXiv preprint arXiv:2012.12919},
  year   = {2024}
}

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