The Optimal Convergence Rate Of The P Version Of The Finite Element Method
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The Optimal Convergence Rate of the P-Version of the Finite Element Method
The p-Version of the finite element method has been previously analyzed for elliptic problems with homogeneous boundary conditions. For a homogeneous condition of the Dirichlet type, it was shown that the exponential asymptotic convergence rate was optimal up to an arbitrarily small positive parameter epsilon. In this paper, an alternate proof is discussed which yields a better estimate by removing the dependence on epsilon. The analysis is extended to treat problems with inhomogeneous boundary conditions of both the Dirichlet and Neumann type. Estimates for a case when the solution has singularities at the corners of the domain are also provided. Keywords: Approximation(Mathematics); Polynomials.
Higher-Order Finite Element Methods
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method
Author: Tadeusz Burczynski
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
During the last two decades the boundary element method has experienced a remarkable evolution. Contemporary concepts and techniques leading to the advancements of capabilities and understanding of the mathematical and computational aspects of the method in mechanics are presented. The special emphasis on theoretical and numerical issues, as well as new formulations and approaches for special and important fields of solid and fluid mechanics are considered. Several important and new mathematical aspects are presented: singularity and hypersingular formulations, regularity, errors and error estimators, adaptive methods, Galerkin formulations, coupling of BEM-FEM and non-deterministic (stochastic and fuzzy) BEM formulations. Novel developments and applications of the boundary element method in various fields of mechanics of solids and fluids are considered: heat conduction, diffusion and radiation, non-linear problems, dynamics and time-depending problems, fracture mechanics, thermoelasticity and poroelasticity, aerodynamics and acoustics, contact problems, biomechanics, optimization and sensitivity analysis problems, ill posed and inverse problems, and identification problems.