We consider a non-self-adjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin metho...

In this paper we introduce a new method for solving partial and ordinary differential equations with large first, second and third derivatives of the solution in some part of the domain using the finite element technique (here called the Galerkin-Gokhman method). The method is based on the application of the Galerkin method to a modified differential equation. The exact solution of the modified...

In recent years, there have been extensive efforts to find the numerical methods for solving problems with interface. The main idea of this work is to introduce an efficient truly meshless method based on the weak form for interface problems. The proposed method combines the direct meshless local Petrov–Galerkin method with the visibility criterion technique to solve the interface problems. It ...

Distributed Generation (DG) in the form of renewable power generation systems is currently preferred for clean power generation. It has a significant impact on the distribution systems. This impact may be either positively or negatively depending on the distribution system, distributed generator and load characteristics. In this works, an overview of DG is briefly introduced. The technology of ...

t-structures, in the abstract, apply to any triangulated category. However, for the most part, they have been studied so far only in the context of sheaves of modules over sites provided with sheaves of rings. In this paper we define and study t-structures for categories of modules over sites provided with sheaves of dgas and E∞-dgas. A close variant, as we show, are the diagonal t-structures t...

A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, dist...

The standing and traveling waves are well known phenomena of the coupled ordinary differential equations in many fields. The wave solutions of the coupled system are considered to be similar to the partial differential equation of the system. In this paper, the waves which appear in a coupled magneto-elastic beam system are discussed theoretically and numerically. The physical system is continu...

We apply the weighted-residual approach recently introduced in [7] to derive dis-continuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods. 1. Introduction. In recent years Discontinuous Galerkin methods have become increasingly popular, and they have ...

Semi-discrete and a family of discrete time locally conservative Dis-continuous Galerkin procedures are formulated for approximations to nonlinear parabolic equations. For the continuous time approximations a priori L 1 (L 2) and L 2 (H 1) estimates are derived and similarly, l 1 (L 2) and l 2 (H 1) for the discrete time schemes. Spatial rates in H 1 and time truncation errors in L 2 are optimal.