Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations

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dc.contributor.authorDraganescu, Andrei
dc.contributor.authorScott, L. Ridgway
dc.date.accessioned2025-10-22T19:58:12Z
dc.date.issued2025-08-31
dc.description.abstractWe introduce a novel technique for proving global strong discrete maximum principles for finite element discretizations of linear and semilinear elliptic equations for cases when the common, matrix-based sufficient conditions are not satisfied. The basic argument consists of extending the strong form of discrete maximum principle from macroelements to the entire domain via a connectivity argument. The method is applied to discretizations of elliptic equations with certain pathological meshes, and to semilinear elliptic equations.
dc.description.urihttp://arxiv.org/abs/2509.00932
dc.format.extent35 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifierdoi:10.13016/m2tcpw-ywoh
dc.identifier.urihttps://doi.org/10.48550/arXiv.2509.00932
dc.identifier.urihttp://hdl.handle.net/11603/40554
dc.language.isoen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.relation.ispartofUMBC Faculty Collection
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectComputer Science - Numerical Analysis
dc.subjectMathematics - Numerical Analysis
dc.titleSufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations
dc.typeText
dcterms.creatorhttps://orcid.org/0009-0001-1425-8374

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