FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2989936686> ?p ?o ?g. }

• W2989936686 endingPage "109109" @default.
• W2989936686 startingPage "109109" @default.
• W2989936686 abstract "In this paper we propose and analyze a weakly nonlinear, energy stable numerical scheme for the strongly anisotropic Cahn-Hilliard model. In particular, a highly nonlinear and singular anisotropic surface energy makes the PDE system very challenging at both the analytical and numerical levels. To overcome this well-known difficulty, we perform a convexity analysis on the anisotropic interfacial energy, and a careful estimate reveals that all its second order functional derivatives stay uniformly bounded by a global constant. This subtle fact enables one to derive an energy stable numerical scheme. Moreover, a linear approximation becomes available for the surface energy part, and a detailed estimate demonstrates the corresponding energy stability. Its combination with an appropriate treatment for the nonlinear double well potential terms leads to a weakly nonlinear, energy stable scheme for the whole system. In particular, such an energy stability is in terms of the interfacial energy with respect to the original phase variable, and no auxiliary variable needs to be introduced. This has important implications, for example, in the case that the method needs to satisfy a maximum principle. More importantly, with a careful application of the global bound for the second order functional derivatives, an optimal rate convergence analysis becomes available for the proposed numerical scheme, which is the first such result in this area. Meanwhile, for a Cahn-Hilliard system with a sufficiently large degree of anisotropy, a Willmore or biharmonic regularization has to be introduced to make the equation well-posed. For such a physical model, all the presented analyses are still available; the unique solvability, energy stability and convergence estimate can be derived in an appropriate manner. In addition, the Fourier pseudo-spectral spatial approximation is applied, and all the theoretical results could be extended for the fully discrete scheme. Finally, a few numerical results are presented, which confirm the robustness and accuracy of the proposed scheme." @default.
• W2989936686 created "2019-12-05" @default.
• W2989936686 creator A5007588049 @default.
• W2989936686 creator A5028411348 @default.
• W2989936686 creator A5061899878 @default.
• W2989936686 date "2020-03-01" @default.
• W2989936686 modified "2023-09-30" @default.
• W2989936686 title "A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis" @default.
• W2989936686 cites W1977032047 @default.
• W2989936686 cites W1987377268 @default.
• W2989936686 cites W1998646725 @default.
• W2989936686 cites W1999107555 @default.
• W2989936686 cites W2014949681 @default.
• W2989936686 cites W2029449803 @default.
• W2989936686 cites W2031651409 @default.
• W2989936686 cites W2031704563 @default.
• W2989936686 cites W2042201895 @default.
• W2989936686 cites W2046528357 @default.
• W2989936686 cites W2048343906 @default.
• W2989936686 cites W2058982054 @default.
• W2989936686 cites W2077001143 @default.
• W2989936686 cites W2083994446 @default.
• W2989936686 cites W2099659360 @default.
• W2989936686 cites W2107714222 @default.
• W2989936686 cites W2109834126 @default.
• W2989936686 cites W2111582391 @default.
• W2989936686 cites W2133418340 @default.
• W2989936686 cites W2135440720 @default.
• W2989936686 cites W2165676519 @default.
• W2989936686 cites W2167347425 @default.
• W2989936686 cites W2167886272 @default.
• W2989936686 cites W2168653054 @default.
• W2989936686 cites W2171628686 @default.
• W2989936686 cites W2317483527 @default.
• W2989936686 cites W2328649268 @default.
• W2989936686 cites W2339407352 @default.
• W2989936686 cites W2410970256 @default.
• W2989936686 cites W2463455424 @default.
• W2989936686 cites W2478263668 @default.
• W2989936686 cites W2500585602 @default.
• W2989936686 cites W2521393946 @default.
• W2989936686 cites W2540267103 @default.
• W2989936686 cites W2553175992 @default.
• W2989936686 cites W2569713119 @default.
• W2989936686 cites W2626341890 @default.
• W2989936686 cites W2740439779 @default.
• W2989936686 cites W2759321824 @default.
• W2989936686 cites W2789307403 @default.
• W2989936686 cites W2911401788 @default.
• W2989936686 cites W2922030862 @default.
• W2989936686 cites W2929974466 @default.
• W2989936686 cites W2945683805 @default.
• W2989936686 cites W2962738836 @default.
• W2989936686 cites W2962906715 @default.
• W2989936686 cites W2963167146 @default.
• W2989936686 cites W2963577202 @default.
• W2989936686 cites W3098605801 @default.
• W2989936686 cites W4232926078 @default.
• W2989936686 doi "https://doi.org/10.1016/j.jcp.2019.109109" @default.
• W2989936686 hasPublicationYear "2020" @default.
• W2989936686 type Work @default.
• W2989936686 sameAs 2989936686 @default.
• W2989936686 citedByCount "16" @default.
• W2989936686 countsByYear W29899366862020 @default.
• W2989936686 countsByYear W29899366862021 @default.
• W2989936686 countsByYear W29899366862022 @default.
• W2989936686 countsByYear W29899366862023 @default.
• W2989936686 crossrefType "journal-article" @default.
• W2989936686 hasAuthorship W2989936686A5007588049 @default.
• W2989936686 hasAuthorship W2989936686A5028411348 @default.
• W2989936686 hasAuthorship W2989936686A5061899878 @default.
• W2989936686 hasBestOaLocation W29899366861 @default.
• W2989936686 hasConcept C105795698 @default.
• W2989936686 hasConcept C106159729 @default.
• W2989936686 hasConcept C121332964 @default.
• W2989936686 hasConcept C134306372 @default.
• W2989936686 hasConcept C145784156 @default.
• W2989936686 hasConcept C154945302 @default.
• W2989936686 hasConcept C158622935 @default.
• W2989936686 hasConcept C162324750 @default.
• W2989936686 hasConcept C182310444 @default.
• W2989936686 hasConcept C186370098 @default.
• W2989936686 hasConcept C191640071 @default.
• W2989936686 hasConcept C24822716 @default.
• W2989936686 hasConcept C2776135515 @default.
• W2989936686 hasConcept C28826006 @default.
• W2989936686 hasConcept C33923547 @default.
• W2989936686 hasConcept C41008148 @default.
• W2989936686 hasConcept C62520636 @default.
• W2989936686 hasConcept C72134830 @default.
• W2989936686 hasConcept C85725439 @default.
• W2989936686 hasConcept C93779851 @default.
• W2989936686 hasConceptScore W2989936686C105795698 @default.
• W2989936686 hasConceptScore W2989936686C106159729 @default.
• W2989936686 hasConceptScore W2989936686C121332964 @default.
• W2989936686 hasConceptScore W2989936686C134306372 @default.
• W2989936686 hasConceptScore W2989936686C145784156 @default.
• W2989936686 hasConceptScore W2989936686C154945302 @default.

• next