We present the Galerkin boundary element method (BEM) for the numerical simulation of free-surface water waves in a model basin. In this work, as a rst step we consider the linearized model of this timedependent three-dimensional problem. After time discretization by an explicit Runge-Kutta scheme, the problem to be solved at each time step corresponds to the evaluation of a Dirichlet-to-Neuman...

We provide a projection-based analysis of a large class of finite element methods for second order elliptic problems. It includes the hybridized version of the main mixed and hybridizable discontinuous Galerkin methods. The main feature of this unifying approach is that it reduces the main difficulty of the analysis to the verification of some properties of an auxiliary, locally defined project...

In this paper we will derive an implicit-explicit (IMEX) finite volume evolution Galerkin scheme for three-dimensional Euler equations. We will in particular concentrate a singular limit of weakly compressible flows when the Mach number is about O(10−2)−O(10−6). In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gr...

We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The velocity (momentum) equation is approximated by a finite element method on div–curl form using the nonconforming Crouzeix– Raviart space. Our main result is that...

A primary cause of failure in microelectronic devices is void growth and movement in aluminum wire interconnects. In addition to thermal and mechanical stress, void evolution is driven by the electric field in the wire. Two new boundary element techniques, approximate Green's functions and Galerkin surface derivative evaluation, have been developed to assist in modeling the electromigration pro...

We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximatio...

Optimal a posteriori error estimates in L∞(0, T ; L(Ω)) are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large class of...

We present a shock-capturing space-time Discontinuous Galerkin method to approximate all speed flows modeled by systems of conservation laws with multiple time scales. The method provides a very general and computationally efficient framework for approximating such systems on account of its ability to incorporate large time steps. Numerical examples ranging from computing the incompressible lim...

For the optimal design and accurate prediction of structural behavior, nonlinear analysis large deformation elastic beams has broad applications in various engineering fields. In this study, equation flexure an beam, also known as elastica, was solved by Galerkin method for a highly solution. The numerical results showed that third-order solution rotation angle at free end beam is more efficien...