Large time step maximum norm regularity of L-stable difference methods for parabolic equations

We establish almost sharp maximum norm regularity properties with large time steps for L-stable finite difference methods for linear second-order parabolic equations with spatially variable coefficients. The regularity properties for first and second spatial differences of the numerical solution mim...

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Bibliographic Details
Published inNumerische Mathematik Vol. 128; no. 3; pp. 551 - 587
Main Author Pruitt, Michael
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
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Summary:We establish almost sharp maximum norm regularity properties with large time steps for L-stable finite difference methods for linear second-order parabolic equations with spatially variable coefficients. The regularity properties for first and second spatial differences of the numerical solution mimic those of the continuous problem, with logarithmic factors in second differences. The regularity results for the inhomogeneous problem imply that the uniform rate of convergence of the numerical solution and its differences is controlled only by the maximum norm of the local truncation error.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-014-0617-1