Displaying similar documents to “A gradient estimate for solutions of the heat equation”

A gradient estimate for solutions of the heat equation. II

Charles S. Kahane (2001)

Czechoslovak Mathematical Journal

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The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.

Global superconvergence of finite element methods for parabolic inverse problems

Hossein Azari, Shu Hua Zhang (2009)

Applications of Mathematics

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In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.