This paper presents a novel objective function for distribution system reconfiguration for reliability enhancement. When islanding operations of distributed generators is prohibited, faults in the feeder interrupt the operation of distributed generators. For this reason, we include the customer interruption cost as well as the distributed generator interruption cost in the objective function in...

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

For problems defined in a two-dimensional domain Ω with boundary conditions specified on a curve Γ, we consider discontinuous Galerkin (DG) schemes with high order polynomial basis functions on a geometry fitting triangular mesh. It is well known that directly imposing the given boundary conditions on a piecewise segment approximation boundary Γh will render any finite element method to be at m...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and fully analyzed for the scalar wave equation in a second order formulation. The dG method considered is motivated by the class of interior penalty dG methods, as well as by the classical work of Hughes and Hulbert [Comput. Methods Appl. Mech. Engrg., 66 (1988), pp. 339–363; Co...

Abstract: In this paper, an arbitrary Lagrangian-Eulerian local discontinuous Galerkin (ALE-LDG) method for Hamilton-Jacobi equations will be developed, analyzed and numerically tested. This method is based on the time-dependent approximation space defined on the moving mesh. A priori error estimates will be stated with respect to the $\mathrm{L}^{\infty}\left(0,T;\mathrm{L}^{2}\left(\Omega\rig...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

We consider in this manuscript  a Timoshenko type beam model with distributed delay term.  If the term is small enough, we prove global existence of solutions by using Faedo-Galerkin approximations together some energy estimates. Under suitable assumptions, exponential stability solution. This result obtained introducing Lyapounov function.

The mixed-potential electric-field integral equation is used in conjunction with the Galerkin’s method and complex image theory for analyzing a transmission line with multiple strips embedded in different layers of a multilayered uniaxially anisotropic dielectric substrate. The two-dimensional Green’s functions for the scalar and vector potentials are analytically obtained in the space domain d...

This paper presents the application of the Successive Galerkin Approximation (SGA) to the Hamilton-Jacobi-Bellman equation to obtain solutions of the optimal attitude control problem. Galerkin's method approximates the value function by a truncated Galerkin series expansion. To do so a truncated Galerkin basis set is formed. A suucient number of functions must be included in this Galerkin basis...