An equilibrated estimator for mixed finite element discretizations of the curl-curl problem

2023/08/03 by T. Chaumont-Frelet, Chaumont-Frelet, T. · 2 citations
Decision Sciences · Engineering · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Fatigue and fracture mechanics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2308.02008

openalex publication_date 2023/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new a posteriori error estimator for mixed finite element discretizations of the curl-curl problem. This estimator relies on a Prager--Synge inequality, and therefore leads to fully guaranteed constant-free upper bounds on the error. The estimator is also locally efficient and polynomial-degree-robust. The construction is based on patch-wise divergence-constrained minimization problems, leading to a cheap embarrassingly parallel algorithm. Crucially, the estimator operates without any assumption on the topology of the domain, and unconventional arguments are required to establish the reliability estimate. Numerical examples illustrate the key theoretical results, and suggest that the estimator is suited for mesh adaptivity purposes.

Cited by

• Some p-robust a posteriori error estimates based on auxiliary spaces
• A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds

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