## Uniform Convergence And Superconvergence Of Mixed Finite Element Methods On Anisotropically Refined Grids

Citations: | 6 - 1 self |

### BibTeX

@MISC{Li_uniformconvergence,

author = {Jichun Li and Mary F. Wheeler},

title = {Uniform Convergence And Superconvergence Of Mixed Finite Element Methods On Anisotropically Refined Grids},

year = {}

}

### OpenURL

### Abstract

The lowest order Raviart-Thomas rectangular element is considered for solving the singular perturbation problem \Gammadiv(arp) + bp = f; where the diagonal tensor a = (" 2 ; 1) or a = (" 2 ; " 2 ): Global uniform convergence rates of O(N \Gamma1 ) for both p and a 1=2 rp in the L 2 - norm are obtained in both cases, where N is the number of intervals in both directions. The pointwise interior (away from the boundary layers) convergence rates of O(N \Gamma1 ) for p are also proved. Superconvergence (i.e., O(N \Gamma2 )) at special points and O(N \Gamma2 ) global L 2 estimate for both p and a 1=2 5 p are obtained by a local postprocessing. Numerical results support our theoretical analysis. Moreover numerical experiments show that an anisotropic mesh gives more accurate results than the standard global uniform mesh.