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Sharply local pointwise a posteriori error estimates for parabolic problems. (English) Zbl 1201.65169

The authors study for the time dependent initial boundary problem
\[ u_{t}-\Delta {u}+ u = f \qquad \text{in}\qquad \Omega \times (o,T] \]
\[ \frac{\partial u}{\partial n}= 0\qquad \text{on}\qquad\partial \Omega, \qquad u(x,0)=u_{0}(x) \]
and the a posteriori local error of the finite element method for approximatingthe solution of this problem. This error estimates are established for the semidiscrete problem and for the fully discrete problem. In both cases the estimates depend on the global error by the space variable.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations

Software:

ALBERTA
PDFBibTeX XMLCite
Full Text: DOI

References:

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