A Family of Methods of the DG-Morley Type for Polyharmonic Equations

Abstract

Discontinuous Galerkin methods as a solution technique of second order elliptic problems, have been increasingly exploited by several authors in the past ten years. It is generally claimed the alledged attractive geometrical flexibility of these methods, although they involve considerable increase of computational effort, as compared to continuous methods. This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic $m$-harmonic equations in a bounded domain of $\mathbb{R}^n$, for $n$ = 2 or $n$ = 3, with $m $$\geq$$ n+1$, as a valid and reasonable alternative to classical finite elements, or even to boundary element methods.