This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods use the backward Euler method for time discretization and interior penalty discontinuous Galerkin methods for spatial discretization. They differ from each other on how the nonlinear term is treated, one of them is bas...

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing t...

computational paradigm DPIV-driven flow simulation: a new Email alerting service here click or sign up in the box at the top right-hand corner of the article Receive free email alerts when new articles cite this article-We present a new approach to simulating unsteady ®uid ®ows, with only very few degrees of freedom, by employing directly eigenmodes extracted from digital particle image velocim...

|Although numerically very e cient the nite element method exhibits di culties whenever the remeshing of the analysis domain must be performed. For such problems utilizing meshless computation methods is very promising. In this paper, a kind of meshless method called the element-free Galerkin method is introduced for electromagnetic eld computation. The mathematical background for the moving le...

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and th...

In the present study, free vibration behaviors of of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) ...

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...

Abstract. This paper is concerned with the analysis of the discontinuous Galerkin finite element method applied to nonstationary convection-diffusion problems with nonlinear convection and nonlinear diffusion. We generalize results from [2], where linear diffusion is assumed. Optimal error estimates are obtained for the L(H) norm and interelement jump terms, however due to the nonlinearity of t...