Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors

We deal with the goal-oriented error estimates and mesh adaptation for nonlinear partial differential equations. The setting of the adjoint problem and the resulting estimates are not based on a differentiation of the primal problem but on a suitable linearization which guarantees the adjoint consis...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2021-07, Vol.93, p.178-198
Main Authors: Dolejší, Vít, Bartoš, Ondřej, Roskovec, Filip
Format: Article
Language:English
Subjects:
Adaptation
Adaptive algorithms
Adaptive solvers
Algebraic errors
Estimates
Goal-oriented error estimates
Iterative methods
Nonlinear differential equations
Nonlinear problems
Partial differential equations
Stopping criteria
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Summary:We deal with the goal-oriented error estimates and mesh adaptation for nonlinear partial differential equations. The setting of the adjoint problem and the resulting estimates are not based on a differentiation of the primal problem but on a suitable linearization which guarantees the adjoint consistency of the numerical scheme. Furthermore, we develop an efficient adaptive algorithm which balances the errors arising from the discretization and the use of nonlinear as well as linear iterative solvers. Several numerical examples demonstrate the efficiency of this algorithm.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2021.04.004