6533b7dafe1ef96bd126e0ec

RESEARCH PRODUCT

A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality

Pekka NeittaanmäkiSvetlana MatculevichSergey Repin

subject

ta113InequalityApplied Mathematicsmedia_common.quotation_subjectta111Numerical Analysis (math.NA)Parabolic partial differential equationExact solutions in general relativityevolutionary reaction-diffusion problemsNorm (mathematics)FOS: MathematicsDiscrete Mathematics and CombinatoricsA priori and a posterioriApplied mathematicsBoundary value problemMathematics - Numerical AnalysisDirichlet–Robin boundary conditionsAnalysisMathematicsmedia_common

description

We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.

yearjournalcountryeditionlanguage
2015-01-01
http://arxiv.org/abs/1312.4361