(2001) A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses....

We investigate the numerical solution of an integro-differential equation with a memory term. For the time discretization we apply the continuous Petrov–Galerkin method considered by Lin et al. [SIAM J. Numer. Anal., 38, 2000]. We combined the Petrov–Galerkin scheme with respect to time with continuous finite elements for the space discretization and obtained a fully discrete scheme. We show op...

(2000) Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/Finite Element ...

In this article we derive local error estimates for some Petrov-Galerkin methods applied to strongly elliptic equations on smooth curves of the plane. The results, e.g., cover the basic first-kind and second-kind integral equations appearing in the boundary element solution of the potential problem. The discretization model includes the Galerkin method and the collocation method using smoothest...

We compare numerically the performance of a new continuous-discontinuous finite element method (CDFEM) for linear convection-diffusion equations with three well-known upwind finite element formulations, namely with the streamline upwind Petrov-Galerkin finite element method, the residualfree bubble method and the discontinuous Galerkin finite element method. The defining feature of the CDFEM is...

In this paper, we uncover and study a new superconvergence property of a large class of finite element methods for one-dimensional convectiondiffusion problems. This class includes discontinuous Galerkin methods defined in terms of numerical traces, discontinuous Petrov–Galerkin methods and hybridized mixed methods. We prove that the so-called numerical traces of both variables superconverge at...

An adaptive mesh refuiement scheme and data shucture has been developed in conjunction with a streamline upwind Petrov-Galerkin finite element formulation for anaiysis of the semiconductor device equations. The nonlinear elecaostatic potential equation and convection dorninated camier current continuity equations are iteratively decoupled in the solution algorithm. Incremental continuation is e...