Qingsong Zou

Analysis of linear and quadratic simplicial finite volume methods for elliptic equations

This paper is devoted to analysis of some convergent properties of both linear and quadratic simplicial finite volume methods (FVMs) for elliptic equations. For linear FVM on domains in any dimensions, the inf-sup condition is established in a simple fashion. It is also proved that the solution of a linear FVM is super-close to that of a relevant finite element method (FEM). As a result, some a posterior error estimates and also algebraic solvers for FEM are extended to FVM. For quadratic FVM on domains in two dimensions, the inf-sup condition is established under some weak condition on the grid.

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 Any Order Finite Volume Schemes for 1D General Elliptic Equations

k

Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems

, the

A Family of Finite Volume Schemes of Arbitrary Order on Rectangular Meshes

2k+1

Is 2k-Conjecture Valid for Finite Volume Methods?

th (or

Polynomial preserving recovery on boundary

2k+1/2

A Recovery Based Linear Finite Element Method For 1D Bi-Harmonic Problems

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.