EFFICIENT AND RELIABLE HIERARCHICAL ERROR ESTIMATES FOR THE DISCRETIZATION ERROR OF ELLIPTIC OBSTACLE PROBLEMS
We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. W...
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| Veröffentlicht in: | Mathematics of computation 2011-01, Vol.80 (273), p.69-88 |
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| creator | KORNHUBER, RALF ZOU, QINGSONG |
| description | We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings. |
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Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.</description><identifier>ISSN: 0025-5718</identifier><identifier>EISSN: 1088-6842</identifier><identifier>CODEN: MCMPAF</identifier><language>eng</language><publisher>Providence, RI: American Mathematical Society</publisher><subject>A posteriori knowledge ; Approximation ; Approximations and expansions ; Cauchy Schwarz inequality ; Coincidence ; Error rates ; Estimate reliability ; Estimators ; Exact sciences and technology ; Heuristics ; Mathematical analysis ; Mathematics ; Methods of scientific computing (including symbolic computation, algebraic computation) ; Numerical analysis ; Numerical analysis. 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Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.</description><subject>A posteriori knowledge</subject><subject>Approximation</subject><subject>Approximations and expansions</subject><subject>Cauchy Schwarz inequality</subject><subject>Coincidence</subject><subject>Error rates</subject><subject>Estimate reliability</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Heuristics</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Methods of scientific computing (including symbolic computation, algebraic computation)</subject><subject>Numerical analysis</subject><subject>Numerical analysis. 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Scientific computation</topic><topic>Sciences and techniques of general use</topic><topic>Triangulation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>KORNHUBER, RALF</creatorcontrib><creatorcontrib>ZOU, QINGSONG</creatorcontrib><collection>Pascal-Francis</collection><jtitle>Mathematics of computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>KORNHUBER, RALF</au><au>ZOU, QINGSONG</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>EFFICIENT AND RELIABLE HIERARCHICAL ERROR ESTIMATES FOR THE DISCRETIZATION ERROR OF ELLIPTIC OBSTACLE PROBLEMS</atitle><jtitle>Mathematics of computation</jtitle><date>2011-01-01</date><risdate>2011</risdate><volume>80</volume><issue>273</issue><spage>69</spage><epage>88</epage><pages>69-88</pages><issn>0025-5718</issn><eissn>1088-6842</eissn><coden>MCMPAF</coden><abstract>We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.</abstract><cop>Providence, RI</cop><pub>American Mathematical Society</pub><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Mathematics of computation, 2011-01, Vol.80 (273), p.69-88 |
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| source | Jstor Complete Legacy; American Mathematical Society Publications; American Mathematical Society Publications (Freely Accessible); EZB-FREE-00999 freely available EZB journals; JSTOR Mathematics & Statistics |
| subjects | A posteriori knowledge Approximation Approximations and expansions Cauchy Schwarz inequality Coincidence Error rates Estimate reliability Estimators Exact sciences and technology Heuristics Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Sciences and techniques of general use Triangulation |
| title | EFFICIENT AND RELIABLE HIERARCHICAL ERROR ESTIMATES FOR THE DISCRETIZATION ERROR OF ELLIPTIC OBSTACLE PROBLEMS |
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