We present a Petrov-Gelerkin (PG) method for class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm on test space as induced by trial norm, i.e., optimal so that inf-sup condition can be satisfied uniformly independent problem. show well-posedness problems under with general assumptions and convection kernels. Second,...

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...

We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using modified transfer and smoothing operators. The estimat...

We investigate an h-p version of the continuous Petrov-Galerkin method for the nonlinear Volterra functional integro-differential equations with vanishing delays. We derive h-p version a priori error estimates in the L-, Hand L-norms, which are completely explicit in the local discretization and regularity parameters. Numerical computations supporting the theoretical results are also presented.

 Abstract : The meshless local Petrov-Galerkin method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for a driven cavity flow for moderate Reynolds numbers using different point distributions. The L2-...