Global Superconvergence of the Lowest-Order Mixed Finite Element on Mildly Structured Meshes

Superconvergence of quadratic finite elements on mildly structured grids

Superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes. For a large class of practically useful grids, the finite element solution uh is proven to be superclose to the interpolant uI and as a result a postprocessing gradient recovery scheme for uh can be devised. Th...

Superconvergence of new mixed finite element spaces

In this paper we prove some superconvergence of a new family of mixed finite element spaces of higher order we introduced in [ETNA, Vol.37, pp.189–201, 2010]. Among all the mixed finite element spaces having optimal order of convergence on quadrilateral grids, this space has the smallest unknowns. However, the scalar variable is only suboptimal in general; thus we have employed a post-processin...

Superconvergence and Postprocessing of Fluxes from Lowest-Order Mixed Methods on Triangles and Tetrahedra

Superconvergence analysis of the linear finite element method and a gradient recovery postprocessing on anisotropic meshes

For the linear finite element method based on general unstructured anisotropic meshes in two dimensions, we establish the superconvergence in energy norm of the finite element solution to the interpolation of the exact solution for elliptic problems. We also prove the superconvergence of the postprocessing process based on the global L2-projection of the gradient of the finite element solution....

Superconvergence of mixed finite element methods for optimal control problems

In this paper, we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods. The state and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Some realistic regularity a...