We examine a nite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral nite elements and prove the convergence of approximate solutions on polyhedral domains in the W 1 2-norm to the true ...

The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L2 and the H1 norms are proved. The numerical solution obtained from the finite element method with quadrature formula is shown to be unique for a sufficien...

Topics Direct Approach for Discrete Systems Strong and Weak Forms for One-Dimensional Problems Second order boundary value problems (1D) Scalar field problems: heat conduction, advection-diffusion Triangular elements Computer implementation Isoparametric elements Numerical integration Vector field problems: elasticity equations Beam elements Eigenvalue problems Time dependent problems Special t...

Abstract:The VLSI design industry has grown rapidly during the last few decades. The complexity of the applications increases day by day due to which the area utilization increases. The tradeoff between area and speed is an important factor. The main focus of continued research has been to increase the operating speed by keeping the area and memory utilization of the design as low as possible. ...

The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of mechanical problems. However, the classical FEM is not well suited for the treatment of large deformation problems since excessive mesh distortions require remeshing. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used t...

This paper describes numerical analyses of the distancedependent gain variation that exists in gain measurements based on the Friis transmission formula for typical broadband antennas, including doubleridged guide horn and log-periodic dipole array antennas. The analyses are performed by simulating gain measurements using the method of moments with higher-order basis functions and the finite in...

The material point method (MPM) has demonstrated itself as a computationally effective particle method for solving solid mechanics problems involving large deformations and/or fragmentation of structures, which are sometimes problematic for finite element methods (FEMs). However, similar to most methods that employ mixed Lagrangian (particle) and Eulerian strategies, analysis of the method is n...

If the nodes for the spectral element method are chosen to be the Gauss-LegendreLobatto points, then the resulting mass matrix is diagonal and the method is sometimes then described as the Gauss-point mass lumped finite element scheme. We study the dispersive behaviour of the scheme issue in detail and provide both a qualitative description of the nature of the dispersive and dissipative behavi...

This paper is an overview of recent developments in the construction of finite element interpolants, which are C-conforming on polygonal domains. In 1975, Wachspress proposed a general method for constructing finite element shape functions on convex polygons. Only recently has renewed interest in such interpolants surfaced in various disciplines including: geometric modeling, computer graphics,...

This paper deals with the application of a moving grid method to the solution of a phase-field model for dendritic growth in twoand three-dimensions. A mesh is found as the solution of an optimization problem that automatically includes the boundary conditions and is solved using a multi-grid approach. The governing equations are discretized in space by linear finite elements and a split time-l...