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Some convergence estimates for semidiscrete type schemes for time-dependent nonselfadjoint parabolic equations

Authors: Ming You Huang and Vidar Thomée
Journal: Math. Comp. 37 (1981), 327-346
MSC: Primary 65M60; Secondary 65M15
MathSciNet review: 628699
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Abstract: ${L_2}$-norm error estimates are shown for semidiscrete (continuous in time) Galerkin finite element type approximations to solutions of general time-dependent nonselfadjoint second order parabolic equations under Dirichlet boundary conditions. The semidiscrete solutions are defined in terms of given methods for the corresponding elliptic problem such as the standard Galerkin method in which the boundary conditions are satisfied exactly but also methods for which this is not necessary. The results are proved by energy arguments and include estimates for the homogeneous equation with both smooth and nonsmooth initial data.

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Article copyright: © Copyright 1981 American Mathematical Society