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Superconvergence of mixed and nonconforming finite element methods

Yuwen Li


In this talk, I will present superconvergence results of mixed and nonconforming finite element methods on some mildly structured or structured grids. These methods include Raviart-Thomas, Hellan-Herrmann-Johnson mixed methods, and Courzeix-Raviart, Rannacher-Turek, Morley nonconforming methods. I will prove some supercloseness estimates, that is, the canonical interpolant and finite element solution are superclose in some norm. Then I will present several recovery operators on irregular triangular grids by using the idea of local least-squares fittings. Finally, I will show that the postprocessed finite element solution from those recovery operators superconverges to the exact solution in theory and experiments.

Tuesday, April 23, 2019
11:00AM AP&M 2402