The motivation for this paper comes from physical problems defined on bounded smooth domains $\Omega$ in 3D. Numerical schemes for these problems are usually defined on some polyhedral domains ${\Omega }_h$ and if there is some additional compactness result available, then the method may converge even if ${\Omega }_h\to \Omega$ only in the sense of compacts. Hence, we use the idea of meshing the whole space and defining the approximative domains as a subset of this partition. Numerical schemes for which quantities are defined on dual partitions...

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the $p$-laplacian kind: $-div\left(\right|\nabla u{|}^{p-2}\nabla u)=f$ (with $1\<p\<\infty$). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the p-Laplacian kind: -div(|∇u|p-2∇u) = ƒ (with 1 < p < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations...