A Family of Methods of the DG-Morley Type for Polyharmonic Equations
Vitoriano Ruas 1*, Jos\'e Henrique Carneiro De Araujo 21 UPMC-Univ.Paris 6, UMR7190 Inst.Jean Le Rond d'Alembert CNRS, Paris, France, Visiting Professor at Graduate School of Computer Science, Universidade Federal Fluminense, Niter'oi, RJ, Brazil
2 Department and Graduate School of Computer Science, Universidade Federal Fluminense, Niter'oi, RJ, Brazil
Received 7 June 2009; Accepted (in revised version) 28 January 2010
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 $\real^n$, 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.AMS subject classifications: 65N30, 65N99, 76D07, 92C55
Key words: Discontinuous Galerkin, finite elements, Hermite tetrahedrons, Morley triangle, non-conforming, polyharmonic equations.
Email: email@example.com (V. Ruas), firstname.lastname@example.org (J. H. Carneiro de Araujo)