期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 35, 期 3, 页码 C173-C193出版社
SIAM PUBLICATIONS
DOI: 10.1137/10081962X
关键词
finite element method; a posteriori; error control; dual problem; adaptivity; automation; nonlinear
资金
- Outstanding Young Investigator grant from the Research Council of Norway [NFR 180450]
- Center of Excellence grant from the Research Council of Norway
This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier-Stokes equations.
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