Adaptive Solution of a Singularly-Perturbed Convection-Diffusion Problem Using a Stabilized Mixed Finite Element Method
We explore the applicability of a new adaptive stabilized dual-mixed finite element method to a singularly-perturbed convection-diffusion equation with mixed boundary conditions. We establish the rate of convergence when the flux and the concentration are approximated, respectively, by Raviart-Thomas/Brezzi-Douglas-Marini and continuous piecewise polynomials. We consider a simple a posteriori error indicator and provide some numerical experiments that illustrate the performance of the method.
The research of the first author was partially supported by MICINN grant MTM2016-76497-R. The research of the second author was supported by the Basque Government through the BERC 2014-2017 programme and by the Spanish Ministry of Economy and Competitivity through the BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
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