The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order ...

In this paper we investigate the feasibility of using the ultra weak variational formulation (UWVF) to solve the timeharmonic 3D elastic wave propagation problem. The UWVF is a non-polynomial volume based method that uses plane waves as basis functions which reduces the computational burden. More general, the UWVF is a special form of the discontinuous Galerkin method. As a model problem we con...

We propose and analyze a finite element method for a semi– stationary Stokes system modeling compressible fluid flow subject to a Navier– slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nédélec spaces of the first kind. The continuity equation is approximated by a standard piecewise constant upwind discontinuous G...

We present the stability and error analysis of the unified Petrov-Galerkin spectral method, developed in [1], for linear fractional partial differential equations with two-sided derivatives and constant coefficients in any (1 + d)-dimensional space-time hypercube, d = 1, 2, 3, · · · , subject to homogeneous Dirichlet initial/boundary conditions. Specifically, we prove the existence and uniquene...

The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus̃ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline di...

Abstract. We present the stability and error analysis of the unified Petrov-Galerkin spectral method, developed in [29], for linear fractional partial differential equations with two-sided derivatives and constant coefficients in any (1 + d)-dimensional space-time hypercube, d = 1, 2, 3, · · · , subject to homogeneous Dirichlet initial/boundary conditions. Specifically, we prove the existence a...

The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nanofluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi-analytical, closed-form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius...

We present a generalized polynomial chaos method to solve the steady and unsteady heat transfer problems with uncertainty in boundary conditions, diffusivity coefficient and forcing terms. The stochastic inputs and outputs are represented spectrally by employing the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [1]. ...

Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundame...