Simplified Adaptive Mesh Construction for Eigenvalue Analysis by BEM.

Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement

We consider the adaptive lowest-order boundary element method (ABEM) based on isotropic mesh-refinement for the weakly-singular integral equation for the 3D Laplacian. The proposed scheme resolves both, possible singularities of the solution as well as of the given data. The implementation thus only deals with discrete integral operators, i.e. matrices. We prove that the usual adaptive mesh-ref...

Quasi-Optimal Adaptive BEM

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singula...

Adaptive Multilevel BEM for Acoustic Scattering

We study the hand p{versions of the Galerkin boundary element method for integral equations of the rst kind in 2D and 3D which result from the scattering of time harmonic acoustic waves at hard or soft scatterers. We derive an abstract a{posteriori error estimate for indeenite problems which is based on stable multilevel decompositions of our test and trial spaces. The Galerkin error is estimat...

BEM approaches and simplified kinetic models for the analysis of damping in deformable MEMS

Microflows occurring in MEMS are addressed by applying a continuum BEM code for quasi-static Stokes flow accounting for slip boundary condition. Working conditions typical of transition and rarefied flows are treated in a simplified manner by employing a viscosity corrected according to semi-analytical solutions for the linearized BGK model of Couette and Poiseuille flows. Numerical results are...