October 22 – Théophile Chaumont-Frelet: A posteriori error estimates for Maxwell’s equations based on flux quasi-equilibration

Théophile Chaumont-Frelet: Thursday 22 October at 11:00, A415, Inria Paris.

I will present of a novel a posteriori estimator for finite element discretizations of Maxwell’s equations. The construction hinges on a modification of the flux equilibration technique, called quasi-equilibration. The resulting estimator is inexpensive to compute and polynomial-degree-robust, which means that the reliability and efficiency constants are independent of the discretization order.

I will first describe the standard flux equilibration technique for the simpler case of Poisson’s problem, and explain why it is hard to directly apply this idea to Maxwell’s equations. Then, I will present in detail the derivation of the proposed estimator through the quasi-equilibration procedure. Numerical examples highlighting the key features of the estimator will be presented, and followed by concluding remarks.

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