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期刊名称: Applications of Mathematics
Volume:64    Issue:2        Page:129-167
ISSN:0862-7940

On the effect of numerical integration in the finite element solution of an elliptic problem with a nonlinear Newton boundary condition期刊论文

作者: Bartoš Ondřej Feistauer Miloslav Roskovec Filip
DOI:10.21136/AM.2019.0192-18

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页码: 129-167
被引频次: 0
出版者: Springer Berlin Heidelberg,ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS,Springer
期刊名称: Applications of Mathematics
ISSN: 0862-7940
卷期: Volume:64    Issue:2
语言: English
摘要: This paper is concerned with the analysis of the finite element method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained by numerical integration. The theoretical results are verified by numerical experiments.
相关主题: error estimation, 65N15, numerical integration, Theoretical, Mathematical and Computational Physics, Mathematics, nonlinear Newton boundary condition, Optimization, finite element discretization, effect of numerical integration, 65D30, weak solution, Classical and Continuum Physics, Analysis, Mathematical and Computational Engineering, Applications of Mathematics, 65N30, elliptic equation, MATHEMATICS, APPLIED, Finite element method, Boundary value problems, Numerical integration, Functions, Elliptic, Differential equations, Nonlinear, Mathematical research, Research,

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