Spurious solutions for high-order curl problems

Document Type

Article

Publication Date

5-2023

Department

Department of Mathematical Sciences

Abstract

We investigate numerical solutions of high-order problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spurious solutions, while mixed formulations with finite elements in complexes solve the problems correctly. To explain the numerical results, we clarify the cohomological structures in high-order problems by relating the partial differential equations to the Hodge-Laplacian boundary problems of the complexes.

Publication Title

IMA Journal of Numerical Analysis

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