An Optimal Transport Based hr-Adaptive Mesh Pursuit
Résumé
This research work deals with error estimation and mesh adaptation in finite element simulations. The finite element method introduces errors compared to the exact solution when solving partial differential equations, and it is crucial to identify, control and reduce them to obtain a reliable numerical approximation. We propose to use optimal transport techniques for mesh adaptation, by relocating mesh vertices based on local error indicators to their optimal position, thus yielding error-conscious mesh adjustments. Numerical experiments are provided to illustrate the performance of the proposed approach.
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