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Randolph E. Bank
Philip E. Gill
Michael Holst

Administrative Contact:
Terry Le

Office: AP&M 7431
Phone: (858)534-9813
Fax: (858)534-5273
E-mail: tele@ucsd.edu
Superconvergence Recovery of Raviart-Thomas Mixed Finite Elements on Irregular Triangulations

Yuwen Li


In this talk, I will describe my results on superconvergence estimates of mixed methods using Raviart--Thomas finite elements. First I prove the canonical interpolant and finite element solution approximating the vector variable are superclose in $L^2$ norm. The main tool is a triangular integral identity in Bank and Xu SIAM J. Numer. Anal 41 (2003) 2294-2312, and a discrete Helmholtz decomposition. Comparing to previous supercloseness results (eg. Brandts Numer. Math. 68 (1994) 311--324), my proof is constructive and works on irregular triangular meshes. Even on a special uniform grid, my result shows that the previous supercloseness result is suboptimal. Next I will describe several postprocessing operators based on simple edge averaging, $L^2$ projection or superconvergence patch recovery. Then I will show the postprocessed finite element solution superconverges to the true solution. If time permits, I will also briefly describe applications to Maxwell's equations and generalizations to fourth order elliptic equations.

Tuesday, February 27, 2018
11:00AM AP&M 2402