A Family of Methods of the DG-Morley Type for Polyharmonic Equations (Advances in Applied Mathematics and Mechanics, 2018)
Discontinuous Galerkin methods as a solution technique of second orderelliptic problems, have been increasingly exploited by several authorsin the past ten years. It is generally claimed the alledged attractivegeometrical flexibility of these methods, although they involveconsiderable increase of computational effort, as compared to continuousmethods. This work is aimed at proposing a combination of DGM andnon-conforming finite element methods to solve elliptic $m$-harmonicequations in a bounded domain of $\mathbb{R}^n$, for $n$ = 2 or $n$ = 3,with $m $$≥$$ n+1$, as a valid and reasonable alternative to classicalfinite elements, or even to boundary element methods.