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

Bernkopf, Maximilian; Melenk, Jens Markus

doi:10.1051/m2an/2022026

Record link:

http://hdl.handle.net/20.500.12708/191374

Title:

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

Citation:

Bernkopf, M., & Melenk, J. M. (2023). Optimal convergence rates in L² for a first order system least squares finite element method. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 57(1), 107–141. https://doi.org/10.1051/m2an/2022026

Publisher DOI:

10.1051/m2an/2022026

CatalogPlus:

AC17203084

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Bernkopf, Maximilian
Melenk, Jens Markus

Organisational Unit:

E101-02-1 - Forschungsgruppe Computational Mathematics
E101-02 - Forschungsbereich Numerik

Journal:

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS

ISSN:

2822-7840

Date (published):

2023

Number of Pages:

Publisher:

EDP SCIENCES S A

Peer reviewed:

Yes

Keywords:

Duality argument; Least squares method

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.

Project title:

Doktoratskolleg "Dissipation and Dispersion in Nonlinear Partial Differential Equations": W1245-N25 (FWF - Österr. Wissenschaftsfonds)

Research Areas:

Mathematical and Algorithmic Foundations: 80%
Modeling and Simulation: 20%

Science Branch:

1010 - Mathematik: 100%

License:

CC BY 4.0