Mathematics > Numerical Analysis
[Submitted on 1 Sep 2024
]
Title: The TRUNC element in any dimension and application to a modified Poisson equation
Title: 任何维度中的TRUNC元素及其在修改后的泊松方程中的应用
Abstract: 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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