Spurious solutions for high order curl problems

2021/10/24 by Kaibo Hu, Hu, Kaibo, Qian Zhang +7
Mathematics · Medicine · #35B45 #35Q60 #65N15 #65N30 #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.2110.12481

openalex publication_date 2021/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate numerical solutions of high order curl 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 curl problems by relating the partial differential equations to the Hodge-Laplacian boundary problems of the gradcurl-complexes.

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