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

2018/05/10 by Thomas Führer, Führer, Thomas, Michael Karkulik +1
Engineering · Mathematics · #35F15 #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1805.04147

openalex publication_date 2018/05/10 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We provide new insights into the a priori theory for a time-stepping scheme\nbased on least-squares finite element methods for parabolic first-order\nsystems. The elliptic part of the problem is of general\nreaction-convection-diffusion type. The new ingredient in the analysis is an\nelliptic projection operator defined via a non-symmetric bilinear form,\nalthough the main bilinear form corresponding to the least-squares functional\nis symmetric. This new operator allows to prove optimal error estimates in the\nnatural norm associated to the problem and, under additional regularity\nassumptions, in the L² norm. Numerical experiments are presented which\nconfirm our theoretical findings.\n

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