Superconvergence of triangular quadratic finite element with interpolated coefficients for semilinear parabolic equation
type: Item
instance of: scholarly article
title: Superconvergence of triangular quadratic finite element with interpolated coefficients for semilinear parabolic equation
zbMATH Open document ID: 1121.65097
author: Zhiguang Xiong
author: Chuanmiao Chen
published in: Applied Mathematics and Computation
publication date: 2007-05-14T00:00:00Z
review text: The authors consider the numerical solution of the problem \[ u_t+Au+f(u)=g\text{ in }\Omega \times (0, T),\;u=0\text{ on }\partial \Omega \times (0, T),\;u(x,0)=u_0\text{ in }\Omega,\tag{1} \] where \(\Omega\) is a bounded complex polygonal domain in \(\mathbb{R}^2\), \(A\) is an elliptic operator, \(g \in L^2(\Omega)\), \(f'(u)\geq 0\) and \(f''(u) \in C(\mathbb{R})\). For this purpose they build the spatially semidiscrete approximation of (1) using the triangular quadratic finite element method with interpolated coefficient (ICFEM). Based on a class of orthogonal expansion in triangles, it is shown that ICFEM has superconvergence \(O(h^4\ln h)\) at each vertex and the side midpoints of all triangles.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M20
zbMATH DE Number: 5152402
zbMATH Keywords: semilinear parabolic equation
zbMATH Keywords: finite element method
zbMATH Keywords: triangular quadratic finite element
zbMATH Keywords: superconvergence
zbMATH Keywords: semidiscretization
reviewed by: Vladimir L. Makarov
MaRDI profile type: Publication
full work available at URL: j.amc.2006.05.192
OpenAlex ID: W2051329212
cites work: Superconvergence for triangular finite elements
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DOI: 10.1016/J.AMC.2006.05.192
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description: scientific article; zbMATH DE number 5152402