Korn’s inequalities for piecewise H1 vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

Operator products occur naturally in a range of regularized boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp we have implemented a complete operator algebra that depends on knowledge of the domain, ...

We analyze the h-p version of the bem for mixed Dirichlet Neumann problems of the Laplacian in polyhedral domains. Based on a regularity analysis of the solution in count-ably normed spaces we show that the boundary element Galerkin solution of the h-p version converges exponentially fast on geometrically graded meshes.

We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the threedimensional analysis of the pr...

A new approach to derive a finite element discretisation of PDE equations soley from observations is compared, in terms of approximation accuracy, with the standard finite element Galerkin approach which assumes knowledge of the governing PDE’s. It is shown both in theory and by means of an example that, for a given model order, the identified model is more accurate than the equivalent finite e...

Korn’s inequalities for piecewise H1 vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

Article history: Received 10 February 2015 Received in revised form 30 June 2015 Accepted 17 July 2015 Available online 28 July 2015

We present new a priori error analyses of the coupling of the Raviart–Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary vari...

We present the Galerkin boundary element method (BEM) for the numerical simulation of free-surface water waves in a model basin. In this work, as a rst step we consider the linearized model of this timedependent three-dimensional problem. After time discretization by an explicit Runge-Kutta scheme, the problem to be solved at each time step corresponds to the evaluation of a Dirichlet-to-Neuman...

Higher order and spectral methods have been used with success for elliptic and parabolic initial and boundary value problems with smooth solutions. On the other hand, higher order methods have been applied to hyperbolic problems with less success, as higher order approximations of discontinuous solutions suffer from the Gibbs phenomenon. We extend past work and show that spectral methods yield ...