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Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data. (English) Zbl 0634.65110
For semilinear parabolic equations with nonsmooth initial data the authors discuss the effect of smoothing properties of the solution operator on the accuracy of Galerkin finite-element approximations. It has been known for several years that for linear parabolic equations the accuracy of Galerkin approximations at any positive time is independent of the degree of the initial data. It is shown here that for the semilinear case the accuracy at positive time reflects a gain in smoothness by two orders as measured by the norm in a Sobolev space. In constrast to the linear case the gain is limited to being no more than two orders.
Reviewer: G.Hedstrom

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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