Matches in SemOpenAlex for { <https://semopenalex.org/work/W1971340088> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W1971340088 endingPage "2391" @default.
- W1971340088 startingPage "2368" @default.
- W1971340088 abstract "In this paper, we extend the work in [W. Cao, Math. Comp., to appear] to functions of n dimensions. We measure the anisotropic behavior of higher-order derivative tensors by the “largest” (in certain sense) ellipse/ellipsoid contained in the level curve/surface of the polynomial for directional derivatives. Given the anisotropic measure for the interpolated functions, we derive an error estimate for piecewise polynomial interpolations on meshes that are quasi-uniform under a given metric. By using the inertia properties for matrix eigenvalues [R. C. Thompson, J. Math. Anal. Appl., 58 (1977), pp. 572–577] and Hölder's inequality, we can identify the optimal mesh metrics leading to the smallest error bound in various norms. Furthermore, we develop a dimensional reduction method to find the anisotropic measure approximately. We present two numerical examples for linear and quadratic interpolation on various anisotropic meshes generated with the optimal mesh metrics developed in this paper. Numerical results show that the smallest interpolation error is attained exactly on meshes optimal for the corresponding error norm as predicted." @default.
- W1971340088 created "2016-06-24" @default.
- W1971340088 creator A5021695845 @default.
- W1971340088 date "2007-01-01" @default.
- W1971340088 modified "2023-09-29" @default.
- W1971340088 title "An Interpolation Error Estimate on Anisotropic Meshes in ${mathcalR}^{n}$ and Optimal Metrics for Mesh Refinement" @default.
- W1971340088 cites W1973071447 @default.
- W1971340088 cites W1975932797 @default.
- W1971340088 cites W1979518155 @default.
- W1971340088 cites W1992595544 @default.
- W1971340088 cites W2003049157 @default.
- W1971340088 cites W2030982479 @default.
- W1971340088 cites W2032350951 @default.
- W1971340088 cites W2042199582 @default.
- W1971340088 cites W2044892973 @default.
- W1971340088 cites W2064364918 @default.
- W1971340088 cites W2071415238 @default.
- W1971340088 cites W2072559684 @default.
- W1971340088 cites W2081179467 @default.
- W1971340088 cites W2091354775 @default.
- W1971340088 cites W2106828713 @default.
- W1971340088 cites W2136969662 @default.
- W1971340088 cites W2142693250 @default.
- W1971340088 doi "https://doi.org/10.1137/060667992" @default.
- W1971340088 hasPublicationYear "2007" @default.
- W1971340088 type Work @default.
- W1971340088 sameAs 1971340088 @default.
- W1971340088 citedByCount "26" @default.
- W1971340088 countsByYear W19713400882012 @default.
- W1971340088 countsByYear W19713400882014 @default.
- W1971340088 countsByYear W19713400882015 @default.
- W1971340088 countsByYear W19713400882016 @default.
- W1971340088 countsByYear W19713400882017 @default.
- W1971340088 countsByYear W19713400882018 @default.
- W1971340088 countsByYear W19713400882020 @default.
- W1971340088 countsByYear W19713400882021 @default.
- W1971340088 countsByYear W19713400882022 @default.
- W1971340088 crossrefType "journal-article" @default.
- W1971340088 hasAuthorship W1971340088A5021695845 @default.
- W1971340088 hasConcept C121684516 @default.
- W1971340088 hasConcept C134306372 @default.
- W1971340088 hasConcept C137800194 @default.
- W1971340088 hasConcept C162324750 @default.
- W1971340088 hasConcept C164660894 @default.
- W1971340088 hasConcept C176217482 @default.
- W1971340088 hasConcept C17744445 @default.
- W1971340088 hasConcept C191795146 @default.
- W1971340088 hasConcept C199539241 @default.
- W1971340088 hasConcept C203616005 @default.
- W1971340088 hasConcept C21547014 @default.
- W1971340088 hasConcept C2524010 @default.
- W1971340088 hasConcept C2780009758 @default.
- W1971340088 hasConcept C28826006 @default.
- W1971340088 hasConcept C31487907 @default.
- W1971340088 hasConcept C33923547 @default.
- W1971340088 hasConcept C41008148 @default.
- W1971340088 hasConcept C502989409 @default.
- W1971340088 hasConcept C77088390 @default.
- W1971340088 hasConceptScore W1971340088C121684516 @default.
- W1971340088 hasConceptScore W1971340088C134306372 @default.
- W1971340088 hasConceptScore W1971340088C137800194 @default.
- W1971340088 hasConceptScore W1971340088C162324750 @default.
- W1971340088 hasConceptScore W1971340088C164660894 @default.
- W1971340088 hasConceptScore W1971340088C176217482 @default.
- W1971340088 hasConceptScore W1971340088C17744445 @default.
- W1971340088 hasConceptScore W1971340088C191795146 @default.
- W1971340088 hasConceptScore W1971340088C199539241 @default.
- W1971340088 hasConceptScore W1971340088C203616005 @default.
- W1971340088 hasConceptScore W1971340088C21547014 @default.
- W1971340088 hasConceptScore W1971340088C2524010 @default.
- W1971340088 hasConceptScore W1971340088C2780009758 @default.
- W1971340088 hasConceptScore W1971340088C28826006 @default.
- W1971340088 hasConceptScore W1971340088C31487907 @default.
- W1971340088 hasConceptScore W1971340088C33923547 @default.
- W1971340088 hasConceptScore W1971340088C41008148 @default.
- W1971340088 hasConceptScore W1971340088C502989409 @default.
- W1971340088 hasConceptScore W1971340088C77088390 @default.
- W1971340088 hasIssue "6" @default.
- W1971340088 hasLocation W19713400881 @default.
- W1971340088 hasOpenAccess W1971340088 @default.
- W1971340088 hasPrimaryLocation W19713400881 @default.
- W1971340088 hasRelatedWork W119710250 @default.
- W1971340088 hasRelatedWork W1495993365 @default.
- W1971340088 hasRelatedWork W1968390457 @default.
- W1971340088 hasRelatedWork W2014261754 @default.
- W1971340088 hasRelatedWork W2045997407 @default.
- W1971340088 hasRelatedWork W2071415238 @default.
- W1971340088 hasRelatedWork W2169113055 @default.
- W1971340088 hasRelatedWork W2337697100 @default.
- W1971340088 hasRelatedWork W2974934677 @default.
- W1971340088 hasRelatedWork W4200536196 @default.
- W1971340088 hasVolume "45" @default.
- W1971340088 isParatext "false" @default.
- W1971340088 isRetracted "false" @default.
- W1971340088 magId "1971340088" @default.
- W1971340088 workType "article" @default.