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.

In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...

This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BKM employs the multiple reciprocity technique. Unlike the method of fundamental solution, the two methods use the non-singular general solution instead of singular f...

In this paper we present a new a posteriori error estimate for the boundary element method applied to an integral equation of the first kind. The estimate is local and sharp for quasi-uniform meshes and so improves earlier work of ours. The mesh-dependence of the constants is analyzed and shown to be weaker than expected from our previous work. Besides the Galerkin boundary element method, the ...

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be pre-calculated and thereby effectively reduces the complexity of the problem to a calculation over the surface. Several eigenvalues are retrieved simultaneously. ...

Model reduction techniques seek approximate solutions of a problem with a large number of DOFs within a subspace of small dimension. Component Mode Synthesis (CMS) methods form a large class of reduction methods where the subspace is selected a priori. Introducing a posteriori error estimation and iterative correction significantly extends the range of applications of reduction methods. The pap...

In both boundary element methods and Trefftz-type finite element methods a partial differential equation in some domain is treated by solving a discrete problem on the boundary of the domain and possibly the boundaries between subdomains. We consider a Trefftz element formulation which is based on the complementary energy functional, and we compare different regularizations of the interelement ...

Electrophysiological modeling of Magnetoand Electro-encephalography (MEG and EEG) rely on accurate forward solvers that relate source activities to sensor measurements. In comparing a Boundary Element (BEM) and a Finite Element Method (FEM) for forward electroencephalography, in our early numerical experiments, we found the FEM to have a better accuracy than the BEM. This triggered a quest to i...