Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors
Numerical Analysis
2023-01-24 v1 Numerical Analysis
Abstract
We consider the goal-oriented error estimates for a linearized iterative solver for nonlinear partial differential equations. For the adjoint problem and iterative solver we consider, instead of the differentiation of the primal problem, a suitable linearization which guarantees the adjoint consistency of the numerical scheme. We derive error estimates and develop an efficient adaptive algorithm which balances the errors arising from the discretization and use of iterative solvers. Several numerical examples demonstrate the efficiency of this algorithm.
Cite
@article{arxiv.2301.09459,
title = {Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors},
author = {Vit Dolejsi and Scott Congreve},
journal= {arXiv preprint arXiv:2301.09459},
year = {2023}
}
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