2 Discretization 9 2.1 The Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Solution Approximation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Weak Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Discrete System . . . . . . . . . . . . . . . . . ....

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...

A new discontinuous Galerkin finite element method for solving diffusion problems is introduced. Unlike the traditional LDG method, the scheme, called the direct discontinuous Galerkin (DDG) method, is based on the direct weak formulation for solutions of parabolic equations in each computational cell, and let cells communicate via the numerical flux ûx ONLY. We propose a general numerical flux...

1 A Model Diffusion Problem . . . . . . . . . . . . . . . . . . . . 1 x.1 Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 1 x.2 Continuous Function . . . . . . . . . . . . . . . . . . . 2 x.3 Normed Vector Space . . . . . . . . . . . . . . . . . . 2 x.4 Square Integrable Function . . . . . . . . . . . . . . . 3 x.5 Inner Product Space . . . . . . . . . . . . . . . . . . . 4 x.6 Cauch...

This paper introduces a novel lowest-order discontinuous Petrov Galerkin (dPG) finite element method (FEM) for the Poisson model problem. The ultra-weak formulation allows for piecewise constant and affine ansatz functions and for piecewise affine and lowest-order Raviart-Thomas test functions. This lowest-order discretization for the Poisson model problem allows for a direct proof of the discr...

<p style='text-indent:20px;'>In this paper, we introduce the weak Galerkin (WG) finite element method for Stokes equations with damping. We establish WG numerical scheme on general meshes and prove well-posedness of scheme. Optimal error estimates velocity pressure are derived. Furthermore, in order to accelerate algorithm, present a two-level give corresponding estimates. Finally, some e...