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Title: Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition (English)
Author: Říhová-Škabrahová, Dana
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 46
Issue: 2
Year: 2001
Pages: 103-144
Summary lang: English
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Category: math
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Summary: The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part $\Gamma \!_1$ of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand side by the explicit Euler method). The scheme we get is linear. The strong convergence of the method is proved under the assumptions that the boundary $\partial \Omega $ is piecewise of class $C^3$ and the initial condition belongs to $L_2$ only. Strong monotonicity and Lipschitz continuity of the form $a(v,w)$ is not an assumption, but a property of this form following from its physical background. (English)
Keyword: finite element method
Keyword: parabolic-elliptic problems
Keyword: two-dimensional electromagnetic field
MSC: 35M10
MSC: 65M12
MSC: 65M60
MSC: 65N30
MSC: 78M10
idZBL: Zbl 1066.65117
idMR: MR1818081
DOI: 10.1023/A:1013783722140
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Date available: 2009-09-22T18:06:07Z
Last updated: 2015-05-19
Stable URL: http://hdl.handle.net/10338.dmlcz/134460
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