the meshless local radial point interpolation (mlrpi) method is applied to examine the magnetohydrodynamic (mhd) ow of third grade uid in a porous medium. the uid saturates the porous space between the two boundaries. several limiting cases of fundamental ows can be obtained as the special cases of present analysis. the variations of pertinent parameters are addressed.

In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines ...

in this paper, three dimensional (3d) static and dynamic analysis of thick plates based on the meshless local petrov-galerkin (mlpg) is presented. using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. a weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

The non-Fourier effect in heat conduction is important in strong thermal environments and thermal shock problems. Generally, commercial FE codes are not available for analysis of non-Fourier heat conduction. In this study, a meshless formulation is presented for the analysis of the non-Fourier heat conduction in the materials. The formulation is based on the symmetric local weak form of the sec...

In this paper, three dimensional (3D) static and dynamic analysis of thick plates based on the Meshless Local Petrov-Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...

We consider the following problem, arising within a geological model of sedimentationerosion: For a given vector field g and a given nonnegative function F defined on a oneor twodimensional domain Ω, find a vector field under the form g̃ = ug, with 0 ≤ u(x) ≤ 1 for a.e. x ∈ Ω, such that divg̃ + F ≥ 0 and (u − 1)(divg̃ + F ) = 0 in Ω. We first give a weak formulation of this problem, and we prove a...

We show that it is possible to apply the DPG methodology without reformulating a second order boundary value problem into a first order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in ad...

In this paper, a weak formulation of the discontinuous variable co-eecient Poisson equation with interfacial jumps is introduced. The existence, uniqueness and regularity of solutions of the Poisson equation are obtained. Finite diierence methods can be derived from the weak formulation. An abstract framework is given for proving convergence of the nite diierence methods for such problems. The ...

A stabilized weak formulation of the radiative transfer equation is presented, which is stable independent of the scattering coeecient. This enables the use of standard nite element discretizations without further algebraic constraints. Furthermore, a weighted residual-based a posteriori error estimate is derived for the discrete solution. An example demonstrates the eeciency of the new method.