A discontinuous hp finite element method for convection—diffusion problems Original Research Article

A discontinuous hp finite element method for convection—diffusion problems Original Research Article Pages 311-341 Carlos Erik Baumann, J. Tinsley Oden Close preview | Related articles | Related reference work articles Abstract | References Abstract This paper presents a new method which exhibits the best features of both finite volume and finite element techniques. Special attention is given to the issues of conservation, flexible accuracy, and stability. The method is elementwise conservative, the order of polynomial approximation can be adjusted element by element, and the stability is not based on the introduction of artificial diffusion, but on the use of a very particular finite element formulation with discontinuous basis functions. The method supports h-, p-, and hp-approximations and can be applied to any type of meshes, including non-matching grids. A priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy.