Norbert Heuer

Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation

In this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a nonlocal quadratic nonlinearity. The analysis is performed for a general fractional order diffusion operator. The nonlinear term studied is a product of the unknown function and a convolution operator of order 0. Convergence of the approximation and a priori error estimates are given. Numerical computations are included, which confirm the theoretical predictions.

Robust DPG Method for Convection-Dominated Diffusion Problems

We propose and analyze a discontinuous Petrov--Galerkin (DPG) method for convection-dominated diffusion problems that provides robust

Additive Schwarz method for the p-version of the boundary element method for the single layer potential operator on a plane screen

L^2

On the h-p version of the boundary element method for Symm's integral equation on polygons

error estimates for the field variables which are quasi-optimal in the energy norm. A key feature of the method is to construct test functions defined by a variational formulation with bilinear form (test norm) specifically designed for the goal of robustness. A main theoretical ingredient is a stability analysis of the adjoint problem. Numerical experiments underline our theoretical results and, in particular, confirm robustness of the DPG method for well-chosen test norms.

A Dual-Dual Formulation for the Coupling of Mixed-FEM and BEM in Hyperelasticity

Summary. We analyze an additive Schwarz preconditioner for the p-version of the boundary element method for the single layer potential operator on a plane screen in the three-dimensional Euclidean space. We decompose the ansatz space, which consists of piecewise polynomials of degree p on a mesh of size h, by introducing a coarse mesh of size

A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms

H\ge h

Exponential convergence of the hp-version for the boundary element method on open surfaces

. After subtraction of the coarse subspace of piecewise constant functions on the coarse mesh this results in local subspaces of piecewise polynomials living only on elements of size H. This decomposition yields a preconditioner which bounds the spectral condition number of the stiffness matrix by

Multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method

O(\log \frac Hhp)^2

The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains

. Numerical results supporting the theory are presented.

Conjugate gradient method for dual-dual mixed formulations

Abstract In this paper, we present the numerical implementation of, and numerical experiments for, the Galerkin approximation of Symms integral equation using the h , p and h - p methods. Numerical results obtained using an adaptive algorithm are also given. The theoretical results for these methods are summarized and are compared with the experimental results.