A Meshless Local Petrov-Galerkin (MLPG) method has been developed for solving 3D elastodynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transien...

A homotopic Galerkin approach to the solution of the Fokker-Planck-Kolmogorov equation is presented. It is argued that the ideal Hilbert Space to approximate the exact solution, ψ∗, is the space L2(dψ) where dψ∗ is the probability measure induced on <n by the solution ψ∗ itself. Since this space is not accessible, it is shown that given an initial approximation sufficiently close to the exact s...

A finite difference/Galerkin spectral discretization for the temporal and spatial fractional coupled Ginzburg–Landau system is proposed analyzed. The Alikhanov L2-1? difference formula utilized to discretize time Caputo derivative, while Legendre-Galerkin approximation used approximate Riesz operator. scheme shown efficiently applicable with accuracy in space second-order time. discrete form of...

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivative...

Abstract. The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth continuous function underlying the dis...

The dispersive properties of hp version discontinuous Galerkin finite element approximation are studied in three different limits. For the small wave-number limit hk → 0, we show the discontinuous Galerkin gives a higher order of accuracy than the standard Galerkin procedure, thereby confirming the conjectures of Hu and Atkins (J. Comput. Phys., 182(2):516– 545, 2002 ). If the mesh is fixed and...

Spline Galerkin approximation methods for the Sherman-Lauricella integral equation on simple closed piecewise smooth contours are studied, and necessary and sufficient conditions for their stability are obtained. It is shown that the method under consideration is stable if and only if certain operators associated with the corner points of the contour are invertible. Numerical experiments demons...

We revisit some results from M. L. Adams [Nucl. Sci. Engrg., 137 (2001), pp. 298– 333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions, and the restrictio...

Using the weighted residual formulation we derive a-posteriori estimates for Discontinuous Galerkin approximations of second order elliptic problems in mixed form. We show that our approach allows to include in a unified way all the methods presented so far in the literature.