QUASI-OPTIMAL APPROXIMATION OF SURFACE BASED LAGRANGE MULTIPLIERS IN FINITE ELEMENT METHODS
We show quasi-optimal a priori convergence results in the L²-and H -1/2 -norm for the approximation of surface based Lagrange multipliers such as those employed in the mortar finite element method. We improve on the estimates obtained in the standard saddle point theory, where error estimates for bo...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2012-01, Vol.50 (4), p.2064-2087 |
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| container_title | SIAM journal on numerical analysis |
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| creator | MELENK, J. M. WOHLMUTH, B. |
| description | We show quasi-optimal a priori convergence results in the L²-and H -1/2 -norm for the approximation of surface based Lagrange multipliers such as those employed in the mortar finite element method. We improve on the estimates obtained in the standard saddle point theory, where error estimates for both the primal and dual variables are obtained simultaneously and thus only suboptimal a priori estimates for the dual variable are reached. For the lowest order case, i.e., k = 1, an additional factor of $\sqrt h |Inh|$ and for higher order cases, i. e., k > 1, an additional factor of $\sqrt h$ in the a priori bound for the dual variable can be recovered. The proof is based on the use of new estimates for the primal variable in strips of width O(h) near these surfaces. |
| doi_str_mv | 10.1137/110832999 |
| format | Article |
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M. ; WOHLMUTH, B.</creator><creatorcontrib>MELENK, J. M. ; WOHLMUTH, B.</creatorcontrib><description>We show quasi-optimal a priori convergence results in the L²-and H -1/2 -norm for the approximation of surface based Lagrange multipliers such as those employed in the mortar finite element method. We improve on the estimates obtained in the standard saddle point theory, where error estimates for both the primal and dual variables are obtained simultaneously and thus only suboptimal a priori estimates for the dual variable are reached. For the lowest order case, i.e., k = 1, an additional factor of $\sqrt h |Inh|$ and for higher order cases, i. e., k > 1, an additional factor of $\sqrt h$ in the a priori bound for the dual variable can be recovered. The proof is based on the use of new estimates for the primal variable in strips of width O(h) near these surfaces.</description><identifier>ISSN: 0036-1429</identifier><identifier>EISSN: 1095-7170</identifier><identifier>DOI: 10.1137/110832999</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>A priori knowledge ; Approximation ; Convergence ; Cylinders ; Decomposition ; Error analysis ; Estimates ; Estimation theory ; Finite element method ; Interfaces ; Interpolation ; Lagrange multiplier ; Lagrange multipliers ; Mathematical analysis ; Mathematical models ; Methods ; Mortars ; Norms ; Point estimators ; Variables</subject><ispartof>SIAM journal on numerical analysis, 2012-01, Vol.50 (4), p.2064-2087</ispartof><rights>Copyright ©2012 Society for Industrial and Applied Mathematics</rights><rights>2012, Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c345t-22742908baa3008b43be496b3b7b1363b698dc60981a2997a5c227cc0a15eaff3</citedby><cites>FETCH-LOGICAL-c345t-22742908baa3008b43be496b3b7b1363b698dc60981a2997a5c227cc0a15eaff3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/41713712$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/41713712$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,3171,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>MELENK, J. M.</creatorcontrib><creatorcontrib>WOHLMUTH, B.</creatorcontrib><title>QUASI-OPTIMAL APPROXIMATION OF SURFACE BASED LAGRANGE MULTIPLIERS IN FINITE ELEMENT METHODS</title><title>SIAM journal on numerical analysis</title><description>We show quasi-optimal a priori convergence results in the L²-and H -1/2 -norm for the approximation of surface based Lagrange multipliers such as those employed in the mortar finite element method. We improve on the estimates obtained in the standard saddle point theory, where error estimates for both the primal and dual variables are obtained simultaneously and thus only suboptimal a priori estimates for the dual variable are reached. For the lowest order case, i.e., k = 1, an additional factor of $\sqrt h |Inh|$ and for higher order cases, i. e., k > 1, an additional factor of $\sqrt h$ in the a priori bound for the dual variable can be recovered. 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| source | SIAM Journals Online; Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| subjects | A priori knowledge Approximation Convergence Cylinders Decomposition Error analysis Estimates Estimation theory Finite element method Interfaces Interpolation Lagrange multiplier Lagrange multipliers Mathematical analysis Mathematical models Methods Mortars Norms Point estimators Variables |
| title | QUASI-OPTIMAL APPROXIMATION OF SURFACE BASED LAGRANGE MULTIPLIERS IN FINITE ELEMENT METHODS |
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