SPEAKER: Theophile Chaumont - French National Institute for computer science and applied mathematics
Location: Only online through TEAMS (see link below)
TITLE: Equilibrated error estimators for curl-curl problems
ABSTRACT :
This talk is dedicated to the design and analysis of a posteriori error estimators based on the concept of flux equilibration. This technology is now well-understood for scalar problems involving the Laplace operator and Lagrange finite elements, but its application to electromagnetic problems associated with the curl-curl operator and Nédélec elements is relatively new. As compared to more traditional (e.g. residual-based) error estimators, equilibrated estimators have two key assets that will be the main focus of the presentation, namely (i) they provide a constant-free upper bound on the discretization error, and (ii) they offer efficiency estimates with polynomial-degree-robust constants, meaning that the quality of the upper bound is not decreased when using high-order elements.
I will first review the concept of flux equilibration in the (simpler) context of the Laplace operator. In particular, I will show that the estimator may be computed from inexpensive, local and uncoupled finite element problems on vertex patches. I will then explain how these ideas can be extended to the curl-curl operator, with application in electromagnetism.
This is a joint work with Alexandre Ern and Martin Vohralík.
