I. Farago, Eotvos Lorand University, Department of Applied Analysis, H-1518, Budapest, Pf. 120, Hungary, e-mail: faragois@cs.elte.hu; S. Korotov, P. Neittaanmaki, University of Jyvaskyla, Department of Mathematical Information Technology, P.O. Box 35, FIN-40014 Jyvaskyla, Finland, e-mail: korotov@mit.jyu.fi (S. Korotov), pn@mit.jyu.fi (P. Neittaanmaki)
Abstract: We solve a linear parabolic equation in $\Bbb R^d$, $d \ge1,$ with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the $\theta$-method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.
Keywords: linear parabolic equation, third boundary condition, finite element method, semidiscretization, fully discretized scheme, elliptic projection
Classification (MSC 2000): 65M60, 65M15
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