New a priori analysis of first-order system least-squares finite element methods for parabolic problems

Führer, Thomas; Karkulik, Michael

Abstract

We provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of the problem is of general reaction-convection-diffusion type. The new ingredient in the analysis is an elliptic projection operator defined via a nonsymmetric bilinear form, although the main bilinear form corresponding to the least-squares functional is symmetric. This new operator allows to prove optimal error estimates in the natural norm associated to the problem and, under additional regularity assumptions, in the L-2 norm. Numerical experiments are presented which confirm our theoretical findings.

Más información

Título según WOS: New a priori analysis of first-order system least-squares finite element methods for parabolic problems
Título según SCOPUS: New a priori analysis of first-order system least-squares finite element methods for parabolic problems
Título de la Revista: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volumen: 35
Número: 5
Editorial: WILEY-BLACKWELL
Fecha de publicación: 2019
Página de inicio: 1777
Página final: 1800
Idioma: English
DOI:

10.1002/num.22376

Notas: ISI, SCOPUS