Comparison Homotopy Perturbation and Adomian Decomposition Techniques for Parabolic Equations

This paper compares homotopy perturbation and Adomian decomposition techniques for the solution of parabolic equations. Some examples are considered to illustrate the techniques. The results reveal that the two techniques gave closed form of solution and as such considered most suitable for solving heat flow problems

Phase-Field Modeling of Droplet Movement using the Discontinuous Finite Element Method

Abstract In this paper, a discontinuous finite element method is presented for the fourth-order nonlinear Cahn-Hilliard equation that models multiphase flows together with the Navier-Stokes equations. A flux scheme suitable for the method is proposed and analyzed together with numerical results. The model is applied to simulate the droplet movement and numerical results are presented

On the negative-order norm accuracy of a local-structure-preserving LDG method

Abstract The accuracy in negative-order norms is examined for a local-structure-preserving local discontinuous Galerkin method for the Laplace equation [Li and Shu, Methods and Applications of Analysis, v13 (2006), pp.215-233]. With its distinctive feature in using harmonic polynomials as local approximating functions, this method has lower computational complexity than the standard local discontinuous Galerkin method while keeping the same order of accuracy in both the energy and the L 2 norms. In this note, numerical experiments are presented to demonstrate some accuracy loss of the method in negative-order norms