Session B6 - Multiresolution and Adaptivity in Numerical PDEs
July 13, 17:00 ~ 17:25 - Room T1
Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
Universität Bonn and Humboldt-Universität zu Berlin, Germany - firstname.lastname@example.org
The talk formulates a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on precomputed fine-scale correctors. The exponential decay of these correctors and their localisation to local patch problems, which depend on the direction of the velocity field and the singular perturbation parameter, is rigorously justified. Under moderate assumptions, this stabilization guarantees stability and quasi-optimal rate of convergence for arbitrary mesh Peclet numbers on fairly coarse meshes at the cost of additional inter-element communication.
Joint work with Guanglian Li (Universität Bonn, Germany) and Daniel Peterseim (Universität Bonn, Germany).