a truly meshless local petrov-galerkin (mlpg) method is developed for solving 3d elasto-static problems. using the general mlpg concept, this method is derived through the local weak forms of the equilibrium equations, by using test functions, namely, the heaviside function. the moving least squares (mls) are chosen to construct the shape functions, for the mlpg method. the penalty approximatio...

When underlying financial variables follow a Markov jump-diffusion process, the value function of a derivative security satisfies a partial integro-differential equation (PIDE) for European-style exercise or a partial integro-differential variational inequality (PIDVI) for American-style exercise. Unless the Markov process has a special structure, analytical solutions are generally not availabl...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

Abstract. We present a Discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG)) which is based on introducing variables defined in the interior and on the boundary of the ...

This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on piecewise constants and a basic upwind flux. For the momentum equation, the method is a new combined discontinuous Galerkin and finite element method approxima...

This paper presents a normed G1 space and a weakened weak (W2) formulation of a cellbased smoothed point interpolation method (CS-PIM) for 2D solid mechanics problems using three-node triangular cells. Displacement fields in the CS-PIM are constructed using the point interpolation method (polynomial PIM or radial PIM) and hence the shape functions possess the Kronecker delta property facilitati...

This paper analyzes a method for solving the thirdand fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov–Galerkin method, which is more reasonable than the standard Galerkin one. The spatial approximation is based on Jacobi polynomials P (α,β) n with α, β ∈ (−1, ∞) and n is the polynomial degree. By choosing appropriate base functions, the resulting system ...