A second order characteristics finite element scheme for natural convection problems

B-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems

In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.

Parallel Adaptive Finite Element Methods for Problems in Natural Convection

A Finite Element Method for Second Order Nonvariational Elliptic Problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solvin...

A Stable Mixed Finite Element Scheme for the Second Order Elliptic Problems

A stable mixed finite element method (MFEM) for the second order elliptic problems, in which the scheme just satisfies the discrete B.B condition, is discussed in this paper. The uniqueness and existence of solutions for the corresponding discrete problems are obtained, and the optimal O(h) order error estimates are derived.

Characteristics finite difference schemes of second order in time for convection-diffusion problems

Two new finite difference schemes based on the method of characteristics are presented for convection-diffusion problems. Both of the schemes are of second order in time, and the matrices of the derived systems of linear equations are symmetric. No numerical integration is required for them. The one is of first order in space and the other is of second order. For the former scheme, an optimal e...