We present an a posteriori error estimate of hierarchical type for the mimetic discretization of elliptic problems. Under a saturation assumption, the global reliability and efficiency of the proposed a posteriori estimator are proved. Several numerical experiments assess the actual performance of the local error indicators in driving adaptive mesh refinement algorithms based on different marking strategies. Finally, we analyze and test an inexpensive variant of the proposed error estimator which drastically reduces the overall computational cost of the adaptive procedures. © 2013 Society for Industrial and Applied Mathematics.
Antonietti, P., BEIRAO DA VEIGA, L., Lovadina, C., Verani, M. (2013). Hierarchical A Posteriori Error Estimators for the Mimetic Discretization of Elliptic Problems. SIAM JOURNAL ON NUMERICAL ANALYSIS, 51(1), 654-675 [10.1137/120873157].
Hierarchical A Posteriori Error Estimators for the Mimetic Discretization of Elliptic Problems
BEIRAO DA VEIGA, LOURENCOSecondo
;
2013
Abstract
We present an a posteriori error estimate of hierarchical type for the mimetic discretization of elliptic problems. Under a saturation assumption, the global reliability and efficiency of the proposed a posteriori estimator are proved. Several numerical experiments assess the actual performance of the local error indicators in driving adaptive mesh refinement algorithms based on different marking strategies. Finally, we analyze and test an inexpensive variant of the proposed error estimator which drastically reduces the overall computational cost of the adaptive procedures. © 2013 Society for Industrial and Applied Mathematics.
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