A discontinuous Galerkin finite element method has been developed to treat the high-order spatial derivatives appearing in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear parabolic partial differential equation, originally proposed to model phase segregation of binary alloys. The developed discontinuous Galerkin approach avoids the need for mixed finite elemen...

A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin finite element method for the generalized 2D vorticity dynamics equations which describe several types of geophysical flows, including the Euler equations. The algorithm consists of a continuous Galerkin finite element method for the stream function and a discontinous Galerkin finite element method for the (p...

We propose and analyze a finite element method for a semi– stationary Stokes system modeling compressible fluid flow subject to a Navier– slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nédélec spaces of the first kind. The continuity equation is approximated by a standard piecewise constant upwind discontinuous G...

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivative...

Time finite element methods are developed for the equations of structural dynamics. The approach employs the time-discontinuous Galerkin method and incorporates stabilizing terms having least-squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time-discontinuous Galerkin and l...

the paper is concerned with a methodology of optimal design of shells of minimum weight with strength, stability and strain constraints. stress and strain state of the shell is determined by galerkin method in the mixed finite element formulation within the geometrically nonlinear theory. the analysis of the effectiveness of different optimization algorithms to solve the set problem is given. t...

Article history: Received 27 January 2014 Received in revised form 22 October 2014 Accepted 26 October 2014 Available online 30 October 2014

Article history: Received 22 November 2012 Received in revised form 13 June 2014 Accepted 1 July 2014 Available online 8 July 2014