Adaptive Crouzeix–Raviart boundary element method

Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method

For the simple layer potential V that is associated with the 3D Laplacian, we consider the weakly singular integral equation V φ = f . This equation is discretized by the lowest order Galerkin boundary element method. We prove convergence of an h-adaptive algorithm that is driven by a weighted residual error estimator. Moreover, we identify the approximation class for which the adaptive algorit...

Adaptive nite element–boundary element solution of boundary value problems

An adaptive nite element–boundary element algorithm is proposed to compute an approximate solution of a given boundary value problem. The convergence in H ( ) is controlled by a boundary element based a-posteriori error estimator from which an adaptive re nement strategy is derived. Corresponding error estimates are given based on appropriate boundary element error estimates in negative Sobolev...

A Regular Indirect Boundary Element Method for Thermal Analysis

A Regular Indirect Boundary Element Method for Thermal Analysis

An Adaptive Finite Element Method

We develop an adaptive nite element algorithm for reactive ow simulations. The underlying equations are the Navier-Stokes equations for low-Mach-number ows and an additional system of convection-diiusion-reaction equations for the chemical species. Especially in combustion problems the reaction terms are very stii and nonlinear. This set of equations represents a complicated system of PDEs whic...