EEorts to develop sinc domain decomposition methods for second-order two-point boundary-value problems have been successful, thus warranting further development of these methods. A logical rst step is to thoroughly investigate the extension of these methods to Poisson's equation posed on a rectangle. The Sinc-Galerkin and sinc-collocation methods are, for appropriate weight choices, identical f...

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(α, u) = 0 for random input α(ω) with almost sure realizations in a ...

In this paper, we study a bybridizable discontinuous Galerkin (HDG) method for the numerical solution of 2D time-harmonic Maxwell’s equations. The formulations are given, and the relationship between the HDG scheme and the upwind flux DG method is also examined. The presented numerical results show the effectiveness of the proposed HDG method especially in comparison to the upwind flux DG metho...

Stochastic Galerkin finite element discretisations of PDEs with stochastically nonlinear coefficients lead to linear systems of equations with block dense matrices. In contrast, stochastic Galerkin finite element discretisations of PDEs with stochastically linear coefficients lead to linear systems of equations with block sparse matrices which are cheaper to manipulate and precondition in the f...

‎In this paper, we discuss about existence of solution for integro-differential system and then we solve it  by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in ...

In this paper we review the existing and develop new local discontinuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develo...

Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.

We discuss the (conjugated) Bubnov–Galerkin and Petrov–Galerkin infinite element (IE) discretizations to Helmholtz equation including the use of elements of locally variable order, optimal choice of IE shape functions, calculation of Echo Area (EA), and automatic hp-adaptivity. The discussion is illustrated with 2D numerical experiments. 2005 Elsevier B.V. All rights reserved. MSC classificatio...

A combined method consisting of the mixed finite element method for flow and the discontinuous Galerkin method for transport is introduced for the coupled system of miscible displacement problem. A “cut-off” operatorM is introduced in the discontinuous Galerkin formular in order to make the combined scheme converge. Optimal error estimates in L(H) for concentration and in L(L) for velocity are ...

In this paper, we apply Shannon wavelet and Galerkin method to deal with the numerical solution of the natural boundary integral equation of plane elasticity probem in the upper half-plane. The fast algorithm is given and only 3K entries need to be computed for one 4K × 4K stiffness matrix. Keyword: plane elasticity problem, natural integral equation, Shannon wavelet, Galerkin-wavelet method.