Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data

Marián Slodička

Displaying similar documents to “Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data”

Semigroup formulation of Rothe's method: application to parabolic problems

Marián Slodička (1992)

Commentationes Mathematicae Universitatis Carolinae

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A semilinear parabolic equation in a Banach space is considered. The purpose of this paper is to show the dependence of an error estimate for Rothe's method on the regularity of initial data. The proofs are done using a semigroup theory and Taylor spectral representation.

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A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations

Martin A. Grepl, Anthony T. Patera (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper, we extend the reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affine parameter dependence. The essential new ingredient is the presence of time in the formulation and solution of the problem – we shall “simply” treat time as an additional, albeit special, parameter. First, we introduce the reduced-basis recipe – Galerkin projection onto a space $W_{N}$ spanned by solutions...