Overlapped Bem-Fem and Some Schwarz Iterations

Convection-adapted BEM-based FEM

We present a new discretization method for homogeneous convectiondiffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness matrices are constructed by means of local boundary element techniques. Our method, which we refer to as a BEM-based FEM, can therefore be considered a local ...

FEM-BEM Couplings without Stabilization

Coupling of Non - Conform Fem and Bem

This paper is concerned with the coupling of non-conform nite element and boundary element methods in continuation of Part I (C. Carstensen, S.A. Funken: Coupling of non-conform nite elements and boundary elements I: a priori estimates), where we recast the interface model problem, introduced a coupling scheme and proved a priori error estimates. In this paper, we establish sharp a posteriori e...

Additive Schwarz Iterations for Markov Chains

A convergence analysis is presented for additive Schwarz iterations when applied to consistent singular systems of equations of the form Ax = b. The theory applies to singular M -matrices with one-dimensional null space and is applicable in particular to systems representing ergodic Markov chains, and to certain discretizations of partial differential equations. Additive Schwarz can be seen as ...

BEM-FEM coupling for wave-structure interaction

We present a numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method and present numerical results that illustrate the accuracy of our scheme.