The finite element solution of second order elliptic problems with the Newton boundary condition

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.

Finite element approximation of fractional order elliptic boundary value problems

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also ...

Mortar Finite Volume Element Approximations of Second Order Elliptic Problems

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...

Multilevel Approaches to Nonconforming Finite Element Discretizations of Linear Second Order Elliptic Boundary Value Problems

We consider adaptive multilevel techniques for nonconforming nite element dis-cretizations of second order elliptic boundary value problems. In particular, we will focus on two basic ingredients of an eecient adaptive algorithm. The rst one is the iterative solution of the arising linear system by preconditioned conjugate gradient methods and the second one is an a posteriori error estimator fo...