| Author | Brian N. Granzow, Assad A. Oberai, and Mark |
|---|---|
| Title | A Non-Uniform Refinement Approach for Solving Adjoint Problems in Functional Error Estimation and Mesh Adaptation |
| Year | 2018 |
| Journal | preprint |
| Pages | 1-13 |
| Abstract | Adjoint-based error estimation is used in finite element methods to effectively and accurately estimate discretization errors in physically meaningful output quantities. These estimates are obtained via the solution of an auxiliary adjoint problem. Obtaining an enriched representation of the solution to this adjoint problem is a necessary step in the process of adjoint-based error estimation. Solving the adjoint problem on a uniformly refined mesh is one possible way to obtain such an enriched adjoint representation. In this note, we propose a similar method for adjoint enrichment, whereby the adjoint problem is solved on a mesh obtained via non-uniform refinement. This leads to an adjoint problem with fewer degrees of freedom than the traditional uniform refinement approach. We propose two possible non-uniform refinement strategies and investigate resulting output error estimates for Poisson's equation in two dimensions and nonlinear elasticity in three dimensions. |
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