Applied and Computational Math Seminar: Error estimates for normal derivatives on boundary concentrated meshes

Speaker:Johannes Pfefferer, Technical University Munich
Title: Error estimates for normal derivatives on boundary concentrated meshes

Abstract: This talk is concerned with finite element error estimates for the solution of linear elliptic equations. More precisely, we focus on approximations and related discretization error estimates for the normal derivative of the solution. In order to illustrate the ideas, we consider the Poisson equation with homogeneous Dirichlet boundary conditions and use standard linear finite elements for its discretization. Approximations of the normal derivatives are introduced in a standard way as well as in a variational sense. On quasi-uniform meshes, one can show that these approximate normal derivatives possess a convergence rate close to one in L^2(\partial\Omega) as long as the singularities due to the corners are mild enough. Using boundary concentrated meshes, we show that the order of convergence can even be doubled in terms of the mesh parameter. As an application, we use these results for the numerical analysis of Dirichlet boundary control problems, where the control variable corresponds to the normal derivative of some adjoint variable. Finally, the predicted convergence rates are confirmed by numerical examples.

Time: Friday, February 23, 2018, 1:30-2:30pm

Place: Exploratory Hall, Room 4106