<div class="csl-bib-body">
<div class="csl-entry">Brunner, M., Innerberger, M., Miraçi, A., Praetorius, D., Streitberger, J., & Heid, P. (2023). Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs. <i>IMA Journal of Numerical Analysis</i>, <i>44</i>(3), 1560–1596. https://doi.org/10.1093/imanum/drad039</div>
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dc.identifier.issn
0272-4979
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/187408
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dc.description.abstract
We consider a general nonsymmetric second-order linear elliptic partial differential equation in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive meshrefinement and the inexact iterative solution of the arising linear systems. More precisely, the iterative solver employs, as an outer loop, the so-called Zarantonello iteration to symmetrize the system and, as an inner loop, a uniformly contractive algebraic solver, for example, an optimally preconditioned conjugate gradient method or an optimal geometric multigrid algorithm. We prove that the proposed inexact adaptive iteratively symmetrized finite element method leads to full linear convergence and, for sufficiently small adaptivity parameters, to optimal convergence rates with respect to the overall computational cost, i.e., the total computational time. Numerical experiments underline the theory.
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dc.description.sponsorship
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.publisher
OXFORD UNIV PRESS
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dc.relation.ispartof
IMA Journal of Numerical Analysis
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
adaptive finite element method
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dc.subject
iterative solver
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dc.subject
nonsymmetric PDEs
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dc.subject
optimal convergence rates
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dc.subject
cost-optimality
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dc.title
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs