Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors
| Autor: | Vít Dolejší, Filip Roskovec, Ondřej Bartoš |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Partial differential equation
Adaptive algorithm Discretization MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Consistency (database systems) Computational Theory and Mathematics Linearization Modeling and Simulation Scheme (mathematics) Applied mathematics 0101 mathematics Algebraic number Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 93:178-198 |
| ISSN: | 0898-1221 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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