Waixiang Cao

Superconvergence of Discontinuous Galerkin Methods for Linear Hyperbolic Equations

In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equations when upwind fluxes are used. We prove, for any polynomial degree

Superconvergence of discontinuous Galerkin methods for two-dimensional hyperbolic equations

k

Superconvergence of Any Order Finite Volume Schemes for 1D General Elliptic Equations

, the

Is 2k-Conjecture Valid for Finite Volume Methods?

2k+1

Superconvergence of immersed finite element methods for interface problems

th (or

Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Schrödinger Equations

2k+1/2

Superconvergence of Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

th) superconvergence rate of the DG approximation at the downwind points and for the domain average under quasi-uniform meshes and some suitable initial discretization. Moreover, we prove that the derivative approximation of the DG solution is superconvergent with a rate

Superconvergence of Immersed Finite Volume Methods for One-Dimensional Interface Problems

k+1

Analysis of a p-version finite volume method for 1D elliptic problems

at all interior left Radau points. All theoretical findings are confirmed by numerical experiments.

Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Hyperbolic Equations

This paper is concerned with superconvergence properties of discontinuous Galerkin (DG) methods for two-dimensional linear hyperbolic conservation laws over rectangular meshes when upwind fluxes are used. We prove, under some suitable initial and boundary discretizations, the (2k+1)th order superconvergence rate of the DG approximation at the downwind points and for the cell averages, when piecewise tensor-product polynomials of degree k are used. Moreover, we prove that the gradient of the DG solution is superconvergent with a rate of (k+1)th order at all interior left Radau points; and the function value approximation is superconvergent at all right Radau points with a rate of (k+2)th order. Numerical experiments indicate that the aforementioned superconvergence rates are sharp.