Matches in SemOpenAlex for { <https://semopenalex.org/work/W2749611175> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2749611175 endingPage "35" @default.
- W2749611175 startingPage "4" @default.
- W2749611175 abstract "We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $dgeq 1$ dimensions. Our main approach consists of taking tools that have been shown to be effective for adaptive boundary element methods and, where necessary, modifying them so that they can be applied to the fractional PDE case. Improved a priori error estimates are derived for the case of quasi-uniform meshes which are seen to deliver sub-optimal rates of convergence owing to the presence of singularities. Attention is then turned to the development of an a posteriori error estimate and error indicators which are suitable for driving an adaptive refinement procedure. We assume that the resulting refined meshes are locally quasi-uniform and develop efficient methods for the assembly of the resulting linear algebraic systems and their solution using iterative methods, including the multigrid method. The storage of the dense matrices along with efficient techniques for computing the dense matrix vector products needed for the iterative solution is also considered. The performance and efficiency of the resulting algorithm is illustrated for a variety of examples." @default.
- W2749611175 created "2017-08-31" @default.
- W2749611175 creator A5068013241 @default.
- W2749611175 creator A5091196582 @default.
- W2749611175 date "2017-12-01" @default.
- W2749611175 modified "2023-10-16" @default.
- W2749611175 title "Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver" @default.
- W2749611175 cites W1190262 @default.
- W2749611175 cites W1972152164 @default.
- W2749611175 cites W1974483840 @default.
- W2749611175 cites W1978321922 @default.
- W2749611175 cites W1980336967 @default.
- W2749611175 cites W1980528419 @default.
- W2749611175 cites W1982739053 @default.
- W2749611175 cites W2009985306 @default.
- W2749611175 cites W2016823491 @default.
- W2749611175 cites W2032532622 @default.
- W2749611175 cites W2039427414 @default.
- W2749611175 cites W2041801153 @default.
- W2749611175 cites W2050871234 @default.
- W2749611175 cites W2055496542 @default.
- W2749611175 cites W2066452322 @default.
- W2749611175 cites W2072045197 @default.
- W2749611175 cites W2081212234 @default.
- W2749611175 cites W2084801628 @default.
- W2749611175 cites W2104339235 @default.
- W2749611175 cites W2105372648 @default.
- W2749611175 cites W2134799749 @default.
- W2749611175 cites W2202081574 @default.
- W2749611175 cites W2532859297 @default.
- W2749611175 doi "https://doi.org/10.1016/j.cma.2017.08.019" @default.
- W2749611175 hasPublicationYear "2017" @default.
- W2749611175 type Work @default.
- W2749611175 sameAs 2749611175 @default.
- W2749611175 citedByCount "74" @default.
- W2749611175 countsByYear W27496111752018 @default.
- W2749611175 countsByYear W27496111752019 @default.
- W2749611175 countsByYear W27496111752020 @default.
- W2749611175 countsByYear W27496111752021 @default.
- W2749611175 countsByYear W27496111752022 @default.
- W2749611175 countsByYear W27496111752023 @default.
- W2749611175 crossrefType "journal-article" @default.
- W2749611175 hasAuthorship W2749611175A5068013241 @default.
- W2749611175 hasAuthorship W2749611175A5091196582 @default.
- W2749611175 hasBestOaLocation W27496111752 @default.
- W2749611175 hasConcept C111472728 @default.
- W2749611175 hasConcept C11413529 @default.
- W2749611175 hasConcept C121332964 @default.
- W2749611175 hasConcept C126255220 @default.
- W2749611175 hasConcept C134306372 @default.
- W2749611175 hasConcept C135628077 @default.
- W2749611175 hasConcept C137119250 @default.
- W2749611175 hasConcept C138885662 @default.
- W2749611175 hasConcept C2524010 @default.
- W2749611175 hasConcept C2778770139 @default.
- W2749611175 hasConcept C28826006 @default.
- W2749611175 hasConcept C31487907 @default.
- W2749611175 hasConcept C33923547 @default.
- W2749611175 hasConcept C41008148 @default.
- W2749611175 hasConcept C75553542 @default.
- W2749611175 hasConcept C93779851 @default.
- W2749611175 hasConcept C97355855 @default.
- W2749611175 hasConceptScore W2749611175C111472728 @default.
- W2749611175 hasConceptScore W2749611175C11413529 @default.
- W2749611175 hasConceptScore W2749611175C121332964 @default.
- W2749611175 hasConceptScore W2749611175C126255220 @default.
- W2749611175 hasConceptScore W2749611175C134306372 @default.
- W2749611175 hasConceptScore W2749611175C135628077 @default.
- W2749611175 hasConceptScore W2749611175C137119250 @default.
- W2749611175 hasConceptScore W2749611175C138885662 @default.
- W2749611175 hasConceptScore W2749611175C2524010 @default.
- W2749611175 hasConceptScore W2749611175C2778770139 @default.
- W2749611175 hasConceptScore W2749611175C28826006 @default.
- W2749611175 hasConceptScore W2749611175C31487907 @default.
- W2749611175 hasConceptScore W2749611175C33923547 @default.
- W2749611175 hasConceptScore W2749611175C41008148 @default.
- W2749611175 hasConceptScore W2749611175C75553542 @default.
- W2749611175 hasConceptScore W2749611175C93779851 @default.
- W2749611175 hasConceptScore W2749611175C97355855 @default.
- W2749611175 hasLocation W27496111751 @default.
- W2749611175 hasLocation W27496111752 @default.
- W2749611175 hasOpenAccess W2749611175 @default.
- W2749611175 hasPrimaryLocation W27496111751 @default.
- W2749611175 hasRelatedWork W1494920804 @default.
- W2749611175 hasRelatedWork W1967605889 @default.
- W2749611175 hasRelatedWork W1987150538 @default.
- W2749611175 hasRelatedWork W2014316689 @default.
- W2749611175 hasRelatedWork W2020922939 @default.
- W2749611175 hasRelatedWork W2113718785 @default.
- W2749611175 hasRelatedWork W2769754504 @default.
- W2749611175 hasRelatedWork W3135525767 @default.
- W2749611175 hasRelatedWork W4213410328 @default.
- W2749611175 hasRelatedWork W4287641365 @default.
- W2749611175 hasVolume "327" @default.
- W2749611175 isParatext "false" @default.
- W2749611175 isRetracted "false" @default.
- W2749611175 magId "2749611175" @default.
- W2749611175 workType "article" @default.