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

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  • We consider evolutionary reaction-diffusion problems 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 the 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.
    Mathematics Subject Classification: 35K20, 65M15, 65N30.


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