In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The moving least-squares (IMLS) approximation is used to establish trial function, and penalty applied enforce boundary conditions, thus final discretized equations of IEFG problems can be obtained by combining with corresponding weak form. influences n...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Matti Leinonen Name of the doctoral dissertation On applying stochastic Galerkin finite element method to electrical impedance tomography Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 135/2015 Field of research Mathematics Manus...

Meshless Finite Element Methods, namely elementfree Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses...

A novel numerical method for solving three-dimensional two phase flow problems is presented. This method combines a quadrature free discontinuous Galerkin method for the level set equation with a pressure stabilized finite element method for the Navier Stokes equations. The main challenge in the computation of such flows is the accurate evaluation of surface tension forces. This involves the co...

We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations for which the approximate velocity field is pointwise divergence-free. The method proposed here builds on the method presented by Labeur and Wells [SIAM J. Sci. Comput., vol. 34 (2012), pp. A889–A913]. We show that with simple modifications of the function spaces in the method of Labeur and ...

We study a hybridizable discontinuous Galerkin method for solving the vorticity-velocity formulation of the Stokes equations in three-space dimensions. We show how to hybridize the method to avoid the construction of the divergence-free approximate velocity spaces, recover an approximation for the pressure and implement the method efficiently. We prove that, when all the unknowns use polynomial...