FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2954888981> ?p ?o ?g. }

• W2954888981 abstract "This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs not applicable for the non-divergence equation, the first-order least-squares formulations naturally have stable weak forms without using integration by parts, allow simple finite element approximation spaces, and have build-in a posteriori error estimators for adaptive mesh refinements. The non-divergence equation is first written as a system of first-order equations by introducing the gradient as a new variable. Then two versions of least-squares finite element methods using simple $C^0$ finite elements are developed in the paper, one is the $L^2$-LSFEM which uses linear elements, the other is the weighted-LSFEM with a mesh-dependent weight to ensure the optimal convergence. Under a very mild assumption that the PDE has a unique solution, optimal a priori and a posteriori error estimates are proved. With an extra assumption on the operator regularity which is weaker than traditionally assumed, convergences in standard norms for the weighted-LSFEM are also discussed. $L^2$-error estimates are derived for both formulations. We perform extensive numerical experiments for smooth, non-smooth, and even degenerate coefficients on smooth and singular solutions to test the accuracy and efficiency of the proposed methods." @default.
• W2954888981 created "2019-07-12" @default.
• W2954888981 creator A5059376708 @default.
• W2954888981 creator A5060613485 @default.
• W2954888981 date "2019-06-27" @default.
• W2954888981 modified "2023-10-18" @default.
• W2954888981 title "Adaptive First-Order System Least-Squares Finite Element Methods for Second Order Elliptic Equations in Non-Divergence Form" @default.
• W2954888981 cites W1555557982 @default.
• W2954888981 cites W1674659126 @default.
• W2954888981 cites W1866311589 @default.
• W2954888981 cites W1965034652 @default.
• W2954888981 cites W1972877576 @default.
• W2954888981 cites W1998803201 @default.
• W2954888981 cites W2007809587 @default.
• W2954888981 cites W2008849850 @default.
• W2954888981 cites W2020552462 @default.
• W2954888981 cites W2041341533 @default.
• W2954888981 cites W2041523977 @default.
• W2954888981 cites W2046300718 @default.
• W2954888981 cites W2071942565 @default.
• W2954888981 cites W2103026454 @default.
• W2954888981 cites W2132292023 @default.
• W2954888981 cites W2200592550 @default.
• W2954888981 cites W2223973105 @default.
• W2954888981 cites W2289792662 @default.
• W2954888981 cites W2330052780 @default.
• W2954888981 cites W2552708984 @default.
• W2954888981 cites W2917203384 @default.
• W2954888981 cites W2963149381 @default.
• W2954888981 cites W2963227054 @default.
• W2954888981 cites W2963671148 @default.
• W2954888981 cites W2963922304 @default.
• W2954888981 cites W3016664815 @default.
• W2954888981 cites W592911714 @default.
• W2954888981 cites W62043397 @default.
• W2954888981 doi "https://doi.org/10.48550/arxiv.1906.11436" @default.
• W2954888981 hasPublicationYear "2019" @default.
• W2954888981 type Work @default.
• W2954888981 sameAs 2954888981 @default.
• W2954888981 citedByCount "3" @default.
• W2954888981 countsByYear W29548889812018 @default.
• W2954888981 countsByYear W29548889812019 @default.
• W2954888981 crossrefType "posted-content" @default.
• W2954888981 hasAuthorship W2954888981A5059376708 @default.
• W2954888981 hasAuthorship W2954888981A5060613485 @default.
• W2954888981 hasBestOaLocation W29548889811 @default.
• W2954888981 hasConcept C105795698 @default.
• W2954888981 hasConcept C111472728 @default.
• W2954888981 hasConcept C121332964 @default.
• W2954888981 hasConcept C134306372 @default.
• W2954888981 hasConcept C135628077 @default.
• W2954888981 hasConcept C138885662 @default.
• W2954888981 hasConcept C144468803 @default.
• W2954888981 hasConcept C162324750 @default.
• W2954888981 hasConcept C185429906 @default.
• W2954888981 hasConcept C207390915 @default.
• W2954888981 hasConcept C2777303404 @default.
• W2954888981 hasConcept C2780586882 @default.
• W2954888981 hasConcept C28826006 @default.
• W2954888981 hasConcept C33923547 @default.
• W2954888981 hasConcept C41895202 @default.
• W2954888981 hasConcept C50522688 @default.
• W2954888981 hasConcept C54067925 @default.
• W2954888981 hasConcept C75553542 @default.
• W2954888981 hasConcept C93779851 @default.
• W2954888981 hasConcept C97355855 @default.
• W2954888981 hasConcept C9936470 @default.
• W2954888981 hasConceptScore W2954888981C105795698 @default.
• W2954888981 hasConceptScore W2954888981C111472728 @default.
• W2954888981 hasConceptScore W2954888981C121332964 @default.
• W2954888981 hasConceptScore W2954888981C134306372 @default.
• W2954888981 hasConceptScore W2954888981C135628077 @default.
• W2954888981 hasConceptScore W2954888981C138885662 @default.
• W2954888981 hasConceptScore W2954888981C144468803 @default.
• W2954888981 hasConceptScore W2954888981C162324750 @default.
• W2954888981 hasConceptScore W2954888981C185429906 @default.
• W2954888981 hasConceptScore W2954888981C207390915 @default.
• W2954888981 hasConceptScore W2954888981C2777303404 @default.
• W2954888981 hasConceptScore W2954888981C2780586882 @default.
• W2954888981 hasConceptScore W2954888981C28826006 @default.
• W2954888981 hasConceptScore W2954888981C33923547 @default.
• W2954888981 hasConceptScore W2954888981C41895202 @default.
• W2954888981 hasConceptScore W2954888981C50522688 @default.
• W2954888981 hasConceptScore W2954888981C54067925 @default.
• W2954888981 hasConceptScore W2954888981C75553542 @default.
• W2954888981 hasConceptScore W2954888981C93779851 @default.
• W2954888981 hasConceptScore W2954888981C97355855 @default.
• W2954888981 hasConceptScore W2954888981C9936470 @default.
• W2954888981 hasLocation W29548889811 @default.
• W2954888981 hasOpenAccess W2954888981 @default.
• W2954888981 hasPrimaryLocation W29548889811 @default.
• W2954888981 hasRelatedWork W1980883473 @default.
• W2954888981 hasRelatedWork W1998397343 @default.
• W2954888981 hasRelatedWork W2004520611 @default.
• W2954888981 hasRelatedWork W2011884938 @default.
• W2954888981 hasRelatedWork W2050829265 @default.
• W2954888981 hasRelatedWork W2147070069 @default.
• W2954888981 hasRelatedWork W2899160247 @default.
• W2954888981 hasRelatedWork W2953869462 @default.
• W2954888981 hasRelatedWork W2954888981 @default.

• next