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.

In this paper, we propose and numerically investigate a family of locally divergence-free central discontinuous Galerkin methods for ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods (SIAM Journal on Numerical Analysis 45 (2007) 2442-2467) for hyperbolic equations, with the use of approximating functions that are exactly dive...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

We show that three well-known \variational crimes" in nite elements { upwinding, mass lumping and selective reduced integration { may be derived from the Galerkin method employing the standard polynomial-based nite element spaces enriched with residual-free bubbles.

this article studied static deflection, natural frequency and nonlinear vibration of a clamped-clamped microbeam under discontinues electrostatic actuation. the electrostatic actuation was induced by applying ac-dc voltage between the microbeam and electrode plate. in contrast to previous works, it was assumed that length of the electrode plate was smaller than that of the microbeam. in additio...

In this paper, we analyze the Lax-Wendroff discontinuous Galerkin (LWDG) method for solving linear conservation laws. The method was originally proposed by Guo et al. in [11], where they applied local discontinuous Galerkin (LDG) techniques to approximate high order spatial derivatives in the Lax-Wendroff time discretization. We show that, under the standard CFL condition τ ≤ λh (where τ and h ...

Several extensions of the family (bivariate) Eyraud-Farlie-Gumbel-Morgenstern copulas (EFGM copulas) are considered. Some them well-known from literature, others have recently been suggested (copulas based on quadratic constructions, some forms convexity, and polynomial copulas). For each these we analyze which properties EFGM preserved (or even improved) (partly) lost. Such can be structural (...

In this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary con...

The compact form of the discontinuous Galerkin method allows for a detailed local analysis of the method in the neighborhood of the shock for a nonlinear model problem. Insight gained from the analysis leads to new ux formulas that are stable and that preserve the compactness of the method. Although developed for a model equation, the ux formulas are applicable to systems such as the Euler equa...