41 research outputs found
Convergence of adaptive mixed finite element method for convection-diffusion-reaction equations
We prove the convergence of an adaptive mixed finite element method (AMFEM)
for (nonsymmetric) convection-diffusion-reaction equations. The convergence
result holds from the cases where convection or reaction is not present to
convection-or reaction-dominated problems. A novel technique of analysis is
developed without any quasi orthogonality for stress and displacement
variables, and without marking the oscillation dependent on discrete solutions
and data. We show that AMFEM is a contraction of the error of the stress and
displacement variables plus some quantity. Numerical experiments confirm the
theoretical results.Comment: arXiv admin note: text overlap with arXiv:1312.645
A posteriori error analysis of multipoint flux mixed finite element methods for interface problems
In this paper, the multipoint flux mixed finite element method is used to approximate the flux of two-dimensional elliptic interface problems. Within the class of modified quasi-monotonically distributed coefficients, we derive uniformly robust residual-type a posteriori error estimators for the flux error. Based on the residual-type estimator, we further develop robust implicit and explicit recovery-type estimators through gradient recovery in H(curl) conforming finite element spaces. Numerical experiments are presented to support the theoretical results