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

Vitoriano Ruas & Jose Henrique Carneiro De Araujo

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 $\real^n$, 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.

  • Keywords

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

  • AMS Subject Headings

65N30 65N99 76D07 92C55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-2-303, author = {Vitoriano Ruas and Jose Henrique Carneiro De Araujo}, 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 $\real^n$, 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.

}, 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 - Vitoriano Ruas & Jose Henrique Carneiro De Araujo 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 KW - finite elements KW - Hermite tetrahedrons KW - Morley triangle KW - non-conforming KW - 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 $\real^n$, 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.

Vitoriano Ruas & Jose 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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