We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparision is made w...

We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator. We propose two methods, post-processing the finite element solutions locally. The new solutions, remaining as optimal-order solutions, are flux-conserving ele...

the impact resistance of new lightweight panel is studied. this panel consists of two thin metal layers bonded together by intermediate fiber/epoxy layers (mcm-sheets). to simulate a behavior of this kind of impact problem, explicit and implicit finite element software abaqus is used. in order to validate the finite element modeling, these results have been compared with experimental test resul...

Dziuk's surface finite element method (FEM) for mean curvature flow has had a significant impact on the development of parametric and evolving FEMs evolution equations flows. However, convergence FEM closed surfaces still remains open since it was proposed in 1990. In this article, we prove semidiscrete with high-order elements surfaces. The proof utilizes matrix-vector formulation monotone str...

in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...