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...

A nodally exact scheme is derived for a model equation in 1D involving zeroth and second order terms. The method is derived using residual-free bubbles in conjunction with the Galerkin approximation. It is shown that this approach leads to the mass lumping scheme for su ciently small mesh sizes. 1. The residual-free bubbles approach. The usage of the Galerkin method enriched with bubble functio...

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element meth...

In a recent paper of Arnold et al. [D.N. Arnold, F. Brezzi, L.D. Marini, A family of discontinuous Galerkin finite elements for the Reissner–Mindlin plate, J. Sci. Comput. 22 (2005) 25–45], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner–Mindlin plate problem. By following t...

In finite element lore the term “unstable discretization” is often applied to situations when approximate solutions develop unphysical “wiggles”, or otherwise behave in a strange manner. A textbook example of such wiggles are Galerkin solutions of a scalar hyperbolic equation with discontinuous data. A more subtle example of instability is the “strange” behavior of mixed finite elements for the...

We discuss stabilized Galerkin approximations in a new framework, widening the scope from the usual dichotomy of the discontinuous Galerkin method on the one hand and Petrov– Galerkin methods such as the SUPG method on the other. The idea is to use interior penalty terms as a means of stabilizing the finite element method using conforming or nonconforming approximation, thus circumventing the n...

In this paper we present a numerical study of the performance of a discontinuous Galerkin formulation for the Navier-Stokes equations. This method is characterized by the fact that the velocity field is approximated using piecewise polynomial functions that are totally discontinuous across interelement boundaries and which are pointwise divergence-free on each element (locally solenoidal). In p...

We present a library for the computation of the shape functions for the element free Galerkin (EFG) method. While the EFG method is in many respects strikingly similar to the finite element method, the construction of the shape functions for the EFG method is much more complicated than in the FEM. Thus, the question arises whether it is possible to encapsulate the complexity of the shape functi...