Volume 2, Issue 3
A Family of Methods of the DG-Morley Type for Polyharmonic Equations

Adv. Appl. Math. Mech., 2 (2010), pp. 303-332.

Published online: 2010-03

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• 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.

• Keywords

Discontinuous Galerkin, finite elements, Hermite tetrahedrons, Morley triangle, non-conforming, polyharmonic equations.

65N30, 65N99, 76D07, 92C55

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@Article{AAMM-2-303, author = {Ruas , Vitoriano and Henrique Carneiro De Araujo , José}, title = {A Family of Methods of the DG-Morley Type for Polyharmonic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {3}, pages = {303--332}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0953}, url = {http://global-sci.org/intro/article_detail/aamm/8333.html} }
TY - JOUR T1 - A Family of Methods of the DG-Morley Type for Polyharmonic Equations AU - Ruas , Vitoriano AU - Henrique Carneiro De Araujo , José JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 303 EP - 332 PY - 2010 DA - 2010/03 SN - 2 DO - http://doi.org/10.4208/aamm.09-m0953 UR - https://global-sci.org/intro/article_detail/aamm/8333.html KW - Discontinuous Galerkin, finite elements, Hermite tetrahedrons, Morley triangle, non-conforming, polyharmonic equations. AB -

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.

Vitoriano Ruas & José Henrique Carneiro De Araujo. (1970). A Family of Methods of the DG-Morley Type for Polyharmonic Equations. Advances in Applied Mathematics and Mechanics. 2 (3). 303-332. doi:10.4208/aamm.09-m0953
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