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...

We present a systematic method for developing low order nonlinear models from physically based, large scale finite element models of rapid thermal processing (RTP) systems. These low order models are extracted from transient results of a detailed finite element model using the proper orthogonal decomposition (POD) method. Eigenfunctions obtained from the POD method are then used as basis functi...

We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) [5], although the numerical implementation differs greatly. Features of the proposed spectral element method inclu...

In this paper, central discontinuous Galerkin methods are developed for solving ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods designed for hyperbolic conservation laws on overlapping meshes, and use different discretization for magnetic induction equations. The resulting schemes carry many features of standard central dis...

The application of finite element methods to problems in structural acoustics ( the vibration of an elastic body coupled to an acoustic fluid medium) is considered. New stabilized methods based on the Hellinger-Reissner variational principle with a generalized least-squares modification are developed which yield improvement in accuracy over the standard Galerkin finite element method for both i...

Sinc-Galerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the Sinc-Galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.The error bound of the method was found. ...

We study in this paper two linearized backward Euler schemes with Galerkin finite element approximations for the time-dependent nonlinear Joule heating equations. By introducing a time-discrete (elliptic) system as proposed in Li and Sun (Int J Numer Anal Model 10:622–633, 2013; SIAM J Numer Anal (to appear)), we split the error function as the temporal error function plus the spatial error fun...

using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-d domains with complex geometry. the petrov-galerkin finite element formulation is adopted to avoid numerical oscillations. turbulence is modeled using the two equation k-ω model. the discretized equations are written in the form o...

Abstract We present a novel geometrically nonlinear EAS element with several desirable features. First, Petrov–Galerkin ansatz significantly improves the element's performance in distorted meshes without loosing simple strain‐driven format. Second, recently proposed mixed integration point strategy is employed to improve robustness Newton–Raphson scheme. Finally and most importantly, we enhance...