Geodesic
Error estimation for finite element solutions on meshes that contain thin elements
Applications of Mathematics, Tome 69 (2024) no. 5, pp. 571-588 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.
DOI : 10.21136/AM.2024.0047-24
Classification : 65D05, 65N30
Keywords: finite element method; triangulation; minimum and maximum angle condition; shape regularity condition; bad triangles 
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Kobayashi, Kenta; Tsuchiya, Takuya. Error estimation for finite element solutions on meshes that contain thin elements. Applications of Mathematics, Tome 69 (2024) no. 5, pp. 571-588. doi: 10.21136/AM.2024.0047-24

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