Polynomial-degree-robust a posteriori error estimation for the curl-curl problem
A talk in the BI.discrete Workshop series by
Martin Vohralik from Inria Paris
| Abstract: | We derive two types of a posteriori error estimates for Nédélec finite element discretizations of the curl-curl problem. In the first case, we proceed by a “broken patchwise equlibration” relying on smaller edge-based patches and related to the localization of the residual with test functions in $H_0(curl)$. In the second case, we design a full equilibration relying on larger vertex-based patches and related to the localization of the residual with test functions in $H(curl)$. The resulting estimators are reliable, locally efficient, polynomial-degree-robust, and constant-free in the second case. Stable extensions of piecewise polynomial data prescribed in a patch of tetrahedra sharing an edge/vertex are a central theoretical tool. In the second case, one has to construct a $H(curl)$-conforming Nédélec piecewise polynomial with a prescribed curl. This is related to a divergence-free decomposition of a given divergence-free $H(div)$-conforming Raviart-Thomas piecewise polynomial. Numerical results illustrate the theoretical developments. This is a joint work with Alexandre Ern (first case) and with Théophile Chaumont-Frelet (both cases). Attendance is only possible after registration with the organizers and with 3G-certificate. Within the CRC this talk is associated to the project(s): A7, B7 |