Error Analysis of Extended Discontinuous Galerkin (XdG) Method
University of Cincinnati / OhioLINK, 2014
Hochschulschrift
Zugriff:
The development of efficient numerical methods to approximate solutions of partial differential equation problems that exhibit high frequency oscillations or boundary layers is a challenging task. One promising approach that has gained considerable popularityin the last decade enriches finite element approximations spaceswith special functions that capture the difficult solution behavior.This extended finite element method or XFEM is usually coupled with continuous finite elements but several recent papers have enrichedthe spaces in discontinuous Galerkin framework.Computational results with this extended discontinuous Galerkin methodor XdG have been successful and been applied to a wide range of application problems. However, very few theoretical error analyses have been done on eitherXFEM or, in particular, XdG.Such analyses are provided in this thesis for the XdG method and appliedto problems with high frequency solutions and others with boundary layers.Proofs are given showing the XdG approximations are more accurate than thosefrom more standard finite element schemes.These results are provided for elliptic and parabolic problems with solutionsthat exhibit high frequency oscillations and elliptic problems where boundary layers are present in the solutions. These error estimates are provided in terms of the degree of the polynomials used in the approximation and the largest high frequency or severity of the boundary layer. Computational results for this new method are presented and confirm the theoretical findings.
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Error Analysis of Extended Discontinuous Galerkin (XdG) Method
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Autor/in / Beteiligte Person: | Toprakseven, Suayip |
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Veröffentlichung: | University of Cincinnati / OhioLINK, 2014 |
Medientyp: | Hochschulschrift |
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