The numerical method for solving the nonlinear eigenvalue problem has been developed by using the collocation Element-Free Galerkin Method (EFGM) and its performance has been numerically investigated. The results of computations show that the approximate solution of the nonlinear eigenvalue problem can be obtained stably by using the developed method. Therefore, it can be concluded that the dev...

A novel nonlinear formulation of finite element and Galerkin methods is presented here, which leads to the Hadamard product expression of the resultant nonlinear algebraic analogue. The presented formulation attains the advantages of weak formulation in the standard finite element and Galerkin schemes and avoids the costly repeated numerical integration of the Jacobian matrix via the recently d...

For the purpose of surgical simulation, we propose an algorithm based upon the Element Free Galerkin method, Total Lagrangian explicit dynamics and nonlinear material formulation. The proposed algorithm does not require a finite element mesh, so is well suited to simulations with irregular geometry. As an example, a simplified 3D simulation of craniotomy induced brain shift including brain, ven...

The paper presents a Galerkin approach for the solution of nonlinear beam equations. The approach is energy consistent, i.e., it is shown that the weighted residual integral describes energy flow. The Galerkin approach gives accurate results with less degrees of freedom as compared to low-order finite element formulation. The Galerkin approach also leads to a nonlinear order-reduction technique...

The paper presents a Galerkin approach for the solution of the nonlinear beam equations. Nonlinear beam analysis is required when analyzing helicopter blades or high-aspect-ratio wings. The present analysis improves on earlier solution techniques based on nonlinear finite element approach used in Refs. 1 and 2, and is the ideal choice for beam-like structures undergoing large motion. Furthermor...

A new nonlinear Galerkin method based on nite element discretization is presented in this paper for a class of second order nonlinear parabolic equations. The new scheme is based on two diierent nite element spaces deened respectively on one coarse grid with grid size H and one ne grid with grid size h H. Nonlinearity and time dependence are both treated on the coarse space and only a xed stati...

We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ∞ L2 error estimates of discontinuous Galerk...

In this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In ...

A space-time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented. The space-time DG method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution. The dispersion and dissipation errors of the scheme are investigated and the algorithm is demonstrated...