Zhiqiang Cai, Cuiyu He, Shun Zhang
Published 2015-10-22Version 1
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the Crouzeix-Raviart nonconforming and the discontinuous Galerkin elements in both two- and three-dimensions, the global reliability bounds are established with constants independent of the jump of the diffusion coefficient. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.
A posteriori error estimates of finite element methods by preconditioning
Convergence and positivity of finite element methods for a haptotaxis model of tumoral invasion
Convergence and supercloseness in a balanced norm of finite element methods on Bakhvalov-type meshes for reaction-diffusion problems
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