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Superconvergent estimates of conforming finite element method for nonlinear time‐dependent Joule heating equations
Author(s) -
Shi Dongyang,
Yang Huaijun
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22202
Subject(s) - superconvergence , finite element method , mathematics , bilinear interpolation , nonlinear system , interpolation (computer graphics) , norm (philosophy) , mixed finite element method , backward euler method , mathematical analysis , euler equations , structural engineering , classical mechanics , statistics , physics , engineering , quantum mechanics , political science , law , motion (physics)
In this article, we study the superconvergence analysis of conforming bilinear finite element method (FEM) for nonlinear Joule heating equations. Based on the rigorous estimates together with high accuracy analysis of this element, mean value technique and interpolation postprocessing approach, the superclose and superconvergent estimates about the related variables in H 1 ‐norm are derived for semidiscrete and a linearized backward Euler fully discrete schemes, which extends the results of optimal estimates obtained for conforming FEMs in the previous literature. At last, a numerical experiment is performed to verify the theoretical analysis.