Fully discrete discontinuous Galerkin methods with variable meshes in time are developed for the fourth order Cahn-Hilliard equation arising from phase transition in materials science. The methods are formulated and analyzed in both two and three dimensions, and are proved to give optimal order error bounds. This coupled with the flexibility of the methods demonstrates that the proposed discont...

In this first part of a series, we propose and analyze, under minimum regularity assumptions, a semi-discrete (in time) scheme and a fully discrete mixed finite element scheme for the Cahn-Hilliard equation ut + ∆(ε∆u − εf(u)) = 0 arising from phase transition in materials science, where ε is a small parameter known as an “interaction length”. The primary goal of this paper is to establish some...

We present and analyze a coupled finite element-boundary element method for a model in stationary micromagnetics. The finite element part is based on mixed conforming elements. For two- and three-dimensional settings, we show well-posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements.