The purpose of the paper is to introduce a novel cell boundary element (CBE) method for the convection dominated diffusion equation. The CBE method can be viewed as a Petrov-Galerkin type method defined on the skeleton of a mesh. The proposed method utilizes continuity of normal flux on each inter-element boundary. By constructing a local basis (mesh-oriented element) that is dependent upon the...

We introduce a max-plus analogue of the Petrov-Galerkin finite element method, to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation, and exploits the properties of projectors on max-plus semimodules. We obtain a nonlinear discretized semigroup, corresponding to a zero-sum two players game. We give an error estimate of order √ ∆t...

The Meshless Local Petrov-Galerkin (MLPG) “mixed collocation” method is applied to the problem of topology-optimization of elastic structures. In this paper, the topic of compliance minimization of elastic structures is pursued, and nodal design variables which represent nodal volume fractions at discretized nodes are adopted. A so-called nodal sensitivity filter is employed, to prevent the phe...

In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in eithe...

Abstract. In this paper we perform an error analysis for a multiscale finite element method for singularly perturbed reaction–diffusion equation. Such method is based on enriching the usual piecewise linear finite element trial spaces with local solutions of the original problem, but do not require these functions to vanish on each element edge. Bubbles are the choice for the test functions all...