Some convergence estimates for semidiscrete type schemes for timedependent nonselfadjoint parabolic equations
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 by Ming You Huang and Vidar Thomée PDF
 Math. Comp. 37 (1981), 327346 Request permission
Abstract:
${L_2}$norm error estimates are shown for semidiscrete (continuous in time) Galerkin finite element type approximations to solutions of general timedependent 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.References

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Additional Information
 © Copyright 1981 American Mathematical Society
 Journal: Math. Comp. 37 (1981), 327346
 MSC: Primary 65M60; Secondary 65M15
 DOI: https://doi.org/10.1090/S00255718198106286991
 MathSciNet review: 628699