Analysis of the vanishing moment method and its finite element approximations for second-order linear elliptic PDEs in non-divergence form

Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs

We prove convergence of adaptive finite element methods (AFEM) for general (nonsymmetric) second order linear elliptic PDE, thereby extending the result of Morin et al [6, 7]. The proof relies on quasi-orthogonality, which accounts for the bilinear form not being a scalar product, together with novel error and oscillation reduction estimates, which now do not decouple. We show that AFEM is a co...

Mortar Finite Volume Element Approximations of Second Order Elliptic 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.

Augmented high order finite volume element method for elliptic PDEs in non-smooth domains: Convergence study

1. Background The Finite Volume ElementMethod (FVEM) is a numerical method for approximating the solution of a partial differential equation (PDE) in a trial function space spanned by piecewise polynomial basis functions, similar to the Finite Element Method (FEM). The coefficients of the linear combination of the basis functions are obtained by imposing the PDE through integrations over contro...

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...