论文信息 - LONG TIME BEHAVIOR OF BACKWARD DIFFERENCE TYPE METHODS FOR PARABOLIC EQUATIONS WITH MEMORY IN BANACH SPACE

LONG TIME BEHAVIOR OF BACKWARD DIFFERENCE TYPE METHODS FOR PARABOLIC EQUATIONS WITH MEMORY IN BANACH SPACE

We show stability in a Banach space framework of backward Euler and second order backward diierence timestepping methods for a parabolic equation with memory. The results are applied to derive maximum norm stability estimates for piecewise linear nite element approximations in a plane spatial domain, which is accomplished by a new resolvent estimate for the discrete Laplacian. Error estimates are also given.

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