Equilibrated error estimators for the magnetostatic problem

Théophile Chaumont-Frelet (INRIA)

Abstract. Beyond its intrinsic physical interest, the magnetostatic problem is mathematically attractive as a model for PDEs involving the curl differential operator. In this talk I will consider a posteriori error estimators for finite element discretizations based on the idea of “flux equilibration”. This technique is well-established in the H1 framework where it leads to guaranteed error upper-bounds and polynomial-degree-robust local lower-bounds. In the H(curl) framework, however, the development of equilibration strategies is much more recent. I will report on two new constructions of equilibrated estimators for the magnetostatic problem. Reliability and efficiency of both estimators will be discussed and illustrated by numerical examples.
This is a joint work with Martin Vohralik.