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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Some convergence estimates for semidiscrete type schemes for time-dependent nonselfadjoint parabolic equations
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by Ming You Huang and Vidar Thomée PDF
Math. Comp. 37 (1981), 327-346 Request permission

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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 327-346
  • MSC: Primary 65M60; Secondary 65M15
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0628699-1
  • MathSciNet review: 628699