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The TRUNC element in any dimension and application to a modified Poisson equation

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arxiv 2409.00748 v1 pith:Q4SHYXET submitted 2024-09-01 math.NA cs.NA

Hongliang Li , Pingbing Ming , Yinghong Zhou This is my paper · ORCID
classification math.NAcs.NA
keywords elementtruncequationerrorestimatemodifiedpoissonsolution
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We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is utilized to approximate a modified Poisson equation defined on a convex polytope, originating from the nonlocal electrostatics model. We have substantiated a uniform error estimate and conducted numerical tests on both the smooth solution and the solution with a sharp boundary layer, which align with the theoretical predictions.

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