Smoothing properties and approximation of time derivatives for parabolic equations: constant time steps |
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Authors: | Yan Yubin |
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Institution: |
1 Department of Mathematics, Chalmers University of Technology and Göteborg University, SE412 96 Göteborg, Sweden
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Abstract: | We study smoothing properties and approximation of time derivativesfor time discretization schemes with constant time steps fora homogeneous parabolic problem formulated as an abstract initial-valueproblem in a Banach space. The time stepping schemes are basedon using rational functions r(z) ez which are A()-stablefor suitable 0, /2] and satisfy |r()| < 1, and the approximationsof time derivatives are based on using difference quotientsin time. Both smooth and non-smooth data error estimates ofoptimal order for the approximation of time derivatives areproved. Further, we apply the results to obtain error estimatesof time derivatives in the supremum norm for fully discretemethods based on discretizing the spatial variable by a finite-elementmethod. |
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Keywords: | Banach space parabolic smoothing time derivative single step time stepping methods fully discrete schemes error estimates finite-element methods |
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