We present a study of the local discontinuous Galerkin method for transient convection-di usion problems in one dimension. We show that p degree piecewise polynomial discontinuous nite element solutions of convection-dominated problems are O( xp+2) superconvergent at Radau points. For di usion-dominated problems, the solution's derivative is O( xp+2) superconvergent at the roots of the derivati...

We construct and analyze a discontinuous Galerkin method to solve advectiondiffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed to automatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is to use consistent weighted average and jump operators. Optimal estimates in the broken graph norm are proven. These are consiste...

In this paper we investigate the relationship between the continuous and the discontinuous Galerkin methods for elliptic problems. In particular, we show that the continuous Galerkin method can be interpreted as the limit of a discontinuous Galerkin method when a stabilization parameter tends to innnity. Based on this observation we derive a method for computing a conservative approximation of ...

We introduce a new and eecient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the Legendre-Galerkin and Chebyshev-Galerkin methods.

The buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates resting on Winkler-Pasternak elastic foundations under in-plane loads for various temperatures is investigated using element-free Galerkin (EFG) method based on first-order shear deformation theory (FSDT). The modified shear correction factor is used based on energy equivalence principle. Carbon ...

In this paper static and dynamic response of nanotweezers composed of two carbon nanotube (CNT) arms are investigated. Taking into account a continuum model and considering the electrostatic actuation as well as the presence of the van der Waals forces, the static nonlinear equations are solved by a step by step linearization and Galerkin projection method. Simulating the closing dynamics of a ...

We summarize several techniques of analysis for finite element methods for linear hyperbolic problems, illustrating their key properties on the simplest model problem. These include the discontinuous Galerkin method, the continuous Galerkin methods on rectangles and triangles, and a nonconforming linear finite element on a special triangular mesh.

This article deals with the computational study of the nonlinear Galerkin method, which is the extension of commonly known Faedo-Galerkin method. The weak formulation of the method is derived and applied to the particular ScottWang-Showalter reaction-diffusion model concerning the problem of combustion of hydrocarbon gases. The proof of convergence of the method based on the method of compactne...

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...

We consider a discontinuous Galerkin finite element method for the advection–reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in ...