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Locally different models in a checkerboard pattern with mesh adaptation and error control for multiple quantities of interest (2405.18567v1)

Published 28 May 2024 in math.NA and cs.NA

Abstract: In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive partial differential equations in a checkerboard pattern, where the solution is continuous across the interface. In addition to the error estimation, the error can be localized using a partition of unity technique. The resulting adaptive algorithm is substantiated with a numerical example.

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