In this paper, a spline finite element approach is manipulated for the numerical solution of an extended system of second-order boundaryvalue problems. The efficiency of the proposed method is examined by comparing the results with the existing exact closed form solution. The numerical results demonstrate that the method is efficient and quite accurate when contrasted with other methods and req...

Finite element methods and the associate collocation methods are considered for solving first-order hyperbolic systems, positive in the sense of Friedrichs. Applied in the case when the meshes are rectangle, those methods lead for example to the successfully used box scheme for the heat equation or D.S.N. scheme for the neutron transport equation. Generalizations of these methods are described ...

This paper addresses the nonlinear elliptic curl–curl equation with uncertainties in the material law. It is frequently employed in the numerical evaluation of magnetostatic fields, where the uncertainty is ascribed to the so–called B–H curve. A truncated Karhunen–Loève approximation of the stochastic B–H curve is presented and analyzed with regard to monotonicity constraints. A stochastic nonl...

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations. Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability an...

For solving electroencephalographic forward problem, coupled method of finite element method FEM and fast moving least square reproducing kernel method FMLSRKM which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed usingmeshfreemethod. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM ...

A simple procedure to formulate efficient and stable hybrid/mixed finite elements is developed, for applications in macroas well as micromechanics. In this method, the strain and displacement field are independently assumed. Instead of using two-field variational principles to enforce both equilibrium and compatibility conditions in a variational sense, the independently assumed element strains...

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlight...

In this paper a new method for solving (non-linear) ordinary differential equations is proposed. The method is based on finite elements (collocation method) as well as on genetic algorithms. The method seems to have some advantages in comparison with the typical sequential (one – step and multi – step) methods. Key-Words: Ordinary Differential Equations, Finite Elements, Genetic Algorithms, Evo...

This paper analyzes triangular finite elements for the preconditioning of Chebyshev collocation solutions of elliptic boundary value problems. Results are given for scalar model problems and for both Stokes and Navier-Stokes equations.