A posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle problems
A variational inequality (VI) and a mixed formulation for an elliptic obstacle problem are considered. Both formulations are discretized by an hp-FE interior penalty discontinuous Galerkin (IPDG) method. In the case of the mixed method, the discrete Lagrange multiplier is a linear combination of bio...
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Published in | Applied numerical mathematics Vol. 76; pp. 76 - 92 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.02.2014
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Subjects | |
Online Access | Get full text |
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Summary: | A variational inequality (VI) and a mixed formulation for an elliptic obstacle problem are considered. Both formulations are discretized by an hp-FE interior penalty discontinuous Galerkin (IPDG) method. In the case of the mixed method, the discrete Lagrange multiplier is a linear combination of biorthogonal basis functions. In particular, also the discrete problems are equivalent. For these formulations a residual based a posteriori error estimate and a hierarchical a posteriori error estimate are derived. For the mixed method the residual based estimate is constructed explicitly, for which the approximation error is split into a discretization error of a linear variational equality problem and additional consistency and obstacle condition terms. For the VI-method a hierarchical estimate based on an overkill solution is derived explicitly. This includes the h–h/2 and p–(p+1)-estimates. The numerical experiments show exponential convergence up to the desired tolerance. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0168-9274 1873-5460 |
DOI: | 10.1016/j.apnum.2013.10.004 |