The meshless element-free Galerkin method was generalized and an algorithm was developed for 3D dynamic modeling of deformable bodies in real time. The efficacy of the algorithm was investigated in a 3D linear viscoelastic model of human spleen subjected to a time-varying compressive force exerted by a surgical grasper. The model remained stable in spite of the considerably large deformations o...

In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternati...

In this paper we present a posteriori error estimators for the approximate solutions of linear parabolic equations. We consider discretizations of the problem by discontinuous Galerkin method in time corresponding to variant Crank-Nicolson schemes and continuous Galerkin method in space. Especially, £nite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson...

Abstract. We consider the first family of H(curl,Ω)-conforming Nedéléc finite elements on tetrahedral meshes. Spectral approximation (p-version) is achieved by keeping the mesh fixed and raising the polynomial degree p uniformly in all mesh cells. We prove that the associated subspaces of discretely weakly divergence free piecewise polynomial vector fields enjoy a long conjectured discrete comp...

Free space Green's functions are derived for graded materials in which the thermal conductivity varies exponentially in one coordinate. Closed form expressions are obtained for the steady state di usion equation, in two and three dimensions. The corresponding boundary integral equation formulations for these problems are derived, and the three-dimensional case is solved numerically using a Gale...

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...

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...

The moving least-square technique is used to construct shape function in the Element Free Galerkin Method at present, but sometimes the algebra equations system obtained from the moving least-square approximation is ill-conditioned and the shape function needs large quantity of inverse operation. In this paper, the weighted orthogonal functions are used as basis ones, the application in the cal...

We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions which guarantee that the continuous problem defines a dissipative dynamical system. We show that, under certain conditions, the discontinuous Galerkin approximation also defines a dissipative dynamical system and we ...

In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The priori error estimates are analyzed under low regularity condition, and robustness with respect to nearly incompressible materials (locking-free) proven. Furthermore, some numerical experiments reported show effectiveness proposed method.