We present a new Boundary Discontinuous Petrov-Galerkin (BDPG) method for Computational Fluid Dynamics (CFD) simulations. The method represents a modification of the standard Hybrid Discontinuous Galerkin (HDG) scheme, and uses locally-computed optimal test functions to achieve enhanced accuracy along the domain boundaries. This leads to improved accuracy in relevant boundary outputs such as li...

A particular meshless method, named meshless local Petrov–Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computa...

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0 D t u+ ∑d i=1 [cli aiD 2μi xi u+cri xiD 2μi bi u]+γ u = ∑d j=1 [κl j a jD 2ν j x j u+κr j x jD 2ν j b j u]+ f , where 2τ ∈ (0, 2), 2μi ∈ (0, 1) and 2ν j ∈ (1, 2), in a (1+d)-dimensional space-time hypercube, d = 1, 2, 3,...

We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the threedimensional analysis of the pr...

A truly meshless Galerkin method is formulated in the present study, as a special case of the general Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. The Galerkin method is implemented as a truly meshless method, for solving elasto-static problems. In the present Galerkin method, the test function is chosen to be the same as the trial function, as a special case of the MLPG approach. Ho...

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magnetoelectric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the...

In this paper we investigate the numerical approximation of fractional diffusion, advection, reaction equation on a bounded interval. Recently explicit form solution to was obtained. Using boundary behavior and Jacobi polynomials, Petrov–Galerkin scheme is proposed analyzed. Numerical experiments are presented which support theoretical results, demonstrate accuracy optimal convergence method.

A fractional step θ-method for the approximation of time dependent viscoelastic fluid flow equations, is described and analyzed in this article. The θ-method implementation allows the velocity and pressure updates to be resolved separately from the stress, reducing the number of unknowns resolved at each step of the method. A streamline upwinded Petrov-Galerkin (SUPG)-method is used to stabiliz...

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0D t u+ ∑d i=1[cli aiD 2μi xi u+ cri xiD 2μi bi u] +γ u = ∑d j=1[ κlj ajD 2νj xj u+κrj xjD 2νj bj u] +f , where 2τ ∈ (0, 2), 2μj ∈ (0, 1) and 2νj ∈ (1, 2), in a (1 +d)-dimensional space-time hypercube, d = 1, 2, 3, · · · ,...