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Keywords:
a posteriori error estimate; $p$-robustness; elliptic problem
Summary:
We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on $p^{1/2}$ only, where $p$ is the discretization polynomial degree. The theoretical results are verified by numerical experiments.
References:
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