Matches in SemOpenAlex for { <https://semopenalex.org/work/W3201582357> ?p ?o ?g. }
- W3201582357 endingPage "111001" @default.
- W3201582357 startingPage "111001" @default.
- W3201582357 abstract "Linearisation is often used as a first step in the analysis of nonlinear initial boundary value problems. The linearisation procedure frequently results in a confusing contradiction where the nonlinear problem conserves energy and has an energy bound but the linearised version does not (or vice versa). In this paper we attempt to resolve that contradiction and relate nonlinear energy conserving and bounded initial boundary value problems to their linearised versions and the related dual problems. We start by showing that a specific skew-symmetric form of the primal nonlinear problem leads to energy conservation and a bound. Next, we show that this specific form together with a non-standard linearisation procedure preserves these properties for the new slightly modified linearised problem. We proceed to show that the corresponding linear and nonlinear dual (or self-adjoint) problems also have bounds and conserve energy due to this specific formulation. Next, the implication of the new formulation on the choice of boundary conditions is discussed. A straightforward nonlinear and linear analysis may lead to a different number and type of boundary conditions required for an energy bound. We show that the new formulation sheds some light on this contradiction. We conclude by illustrating that the new continuous formulation automatically leads to energy stable and energy conserving numerical approximations for both linear and nonlinear primal and dual problems if the approximations are formulated on summation-by-parts form." @default.
- W3201582357 created "2021-09-27" @default.
- W3201582357 creator A5057106073 @default.
- W3201582357 date "2022-04-01" @default.
- W3201582357 modified "2023-09-25" @default.
- W3201582357 title "Nonlinear and linearised primal and dual initial boundary value problems: When are they bounded? How are they connected?" @default.
- W3201582357 cites W1972670182 @default.
- W3201582357 cites W1974961323 @default.
- W3201582357 cites W1976312688 @default.
- W3201582357 cites W1977956169 @default.
- W3201582357 cites W1978484255 @default.
- W3201582357 cites W1981486221 @default.
- W3201582357 cites W1985102833 @default.
- W3201582357 cites W1986274779 @default.
- W3201582357 cites W1988939884 @default.
- W3201582357 cites W1990596161 @default.
- W3201582357 cites W1992812527 @default.
- W3201582357 cites W1996406705 @default.
- W3201582357 cites W2000256143 @default.
- W3201582357 cites W2004993859 @default.
- W3201582357 cites W2005576690 @default.
- W3201582357 cites W2008179816 @default.
- W3201582357 cites W2010222530 @default.
- W3201582357 cites W2019112627 @default.
- W3201582357 cites W2021395669 @default.
- W3201582357 cites W2026986162 @default.
- W3201582357 cites W2027619967 @default.
- W3201582357 cites W2029811565 @default.
- W3201582357 cites W2036965147 @default.
- W3201582357 cites W2037324842 @default.
- W3201582357 cites W2043341868 @default.
- W3201582357 cites W2043465319 @default.
- W3201582357 cites W2049068370 @default.
- W3201582357 cites W2049537509 @default.
- W3201582357 cites W2054391891 @default.
- W3201582357 cites W2055816129 @default.
- W3201582357 cites W2065978762 @default.
- W3201582357 cites W2071447842 @default.
- W3201582357 cites W2072226973 @default.
- W3201582357 cites W2075842486 @default.
- W3201582357 cites W2076605545 @default.
- W3201582357 cites W2082193626 @default.
- W3201582357 cites W2085413857 @default.
- W3201582357 cites W2101506489 @default.
- W3201582357 cites W2102681519 @default.
- W3201582357 cites W2104705102 @default.
- W3201582357 cites W2118241732 @default.
- W3201582357 cites W2123809583 @default.
- W3201582357 cites W2129462040 @default.
- W3201582357 cites W2130112398 @default.
- W3201582357 cites W2130350269 @default.
- W3201582357 cites W2130443691 @default.
- W3201582357 cites W2132307716 @default.
- W3201582357 cites W2136431693 @default.
- W3201582357 cites W2141394518 @default.
- W3201582357 cites W2146156763 @default.
- W3201582357 cites W2153149615 @default.
- W3201582357 cites W2154328412 @default.
- W3201582357 cites W2166998624 @default.
- W3201582357 cites W2528000392 @default.
- W3201582357 cites W2615119937 @default.
- W3201582357 cites W2749971079 @default.
- W3201582357 cites W2951444615 @default.
- W3201582357 cites W2980605003 @default.
- W3201582357 cites W2996615006 @default.
- W3201582357 cites W3006143776 @default.
- W3201582357 cites W3016681167 @default.
- W3201582357 cites W3016981622 @default.
- W3201582357 cites W3095098477 @default.
- W3201582357 cites W3098315804 @default.
- W3201582357 cites W3164887324 @default.
- W3201582357 cites W3182514927 @default.
- W3201582357 cites W92681173 @default.
- W3201582357 doi "https://doi.org/10.1016/j.jcp.2022.111001" @default.
- W3201582357 hasPublicationYear "2022" @default.
- W3201582357 type Work @default.
- W3201582357 sameAs 3201582357 @default.
- W3201582357 citedByCount "3" @default.
- W3201582357 countsByYear W32015823572022 @default.
- W3201582357 countsByYear W32015823572023 @default.
- W3201582357 crossrefType "journal-article" @default.
- W3201582357 hasAuthorship W3201582357A5057106073 @default.
- W3201582357 hasBestOaLocation W32015823571 @default.
- W3201582357 hasConcept C105795698 @default.
- W3201582357 hasConcept C121332964 @default.
- W3201582357 hasConcept C126255220 @default.
- W3201582357 hasConcept C134306372 @default.
- W3201582357 hasConcept C158622935 @default.
- W3201582357 hasConcept C182310444 @default.
- W3201582357 hasConcept C186370098 @default.
- W3201582357 hasConcept C28826006 @default.
- W3201582357 hasConcept C33923547 @default.
- W3201582357 hasConcept C34388435 @default.
- W3201582357 hasConcept C62354387 @default.
- W3201582357 hasConcept C62520636 @default.
- W3201582357 hasConcept C77553402 @default.
- W3201582357 hasConceptScore W3201582357C105795698 @default.
- W3201582357 hasConceptScore W3201582357C121332964 @default.