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

TL;DR

This paper develops a finite element method with multi-goal error estimation and mesh adaptation for solving locally different PDEs arranged in a checkerboard pattern, improving accuracy for multiple quantities of interest.

Contribution

It introduces a dual weighted residual-based error estimation and adaptive mesh refinement tailored for multi-physics problems with discontinuous local models.

Findings

Effective error localization using partition of unity.

Successful adaptive algorithm demonstrated with numerical example.

Enhanced accuracy in multi-quantity PDE solutions.

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.