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arXiv · 1805.04147

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

Thomas Führer·Michael Karkulik
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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 non-symmetric 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.

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Thomas Führer, Michael Karkulik. 2018-05-10. New a priori analysis of first-order system least-squares finite element methods for parabolic problems. https://arxiv.org/abs/1805.04147

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