TITLE

On the development of adaptive random differential quadrature method with an error recovery technique and its application in the locally high gradient problems

AUTHOR(S)
Mulay, Shantanu S.; Hua Li; See, Simon
PUB. DATE
April 2010
SOURCE
Computational Mechanics;Apr2010, Vol. 45 Issue 5, p467
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
An adaptive numerical method called, the adaptive random differential quadrature (ARDQ) method is presented in this paper. In the ARDQ method, the random differential quadrature (RDQ) method is coupled with a posteriori error estimator based on relative error norm in the displacement field. An error recovery technique, based on the least square averaging over the local interpolation domain, is proposed which improves the solution accuracy as the spacing, h ? 0. In the adaptive refinement, a novel convex hull approach with the vectors cross product is proposed to ensure that the newly created nodes are always within the computational domain. The ARDQ method numerical accuracy is successfully evaluated by solving several 1D, 2D and irregular domain problems having locally high gradients. It is concluded from the convergence values that the ARDQ method coupled with error recovery technique can be effectively used to solve the locally high gradient initial and boundary value problems.
ACCESSION #
47924238

 

Related Articles

  • Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative Dependence. Baoqiang Yan; Donal O�??Regan; Ravi Agarwal // Positivity;Nov2007, Vol. 11 Issue 4, p687 

    Abstract  The existence of multiple positive solutions is presented for the singular second-order boundary value problems $$\left\{\begin{array}{ll} x^{\prime\prime}\Phi(t)f(t,x,x') =0, 0 using the fixed point index, where f may be singular at x  =  0 and x�?�...

  • To the Jubilee of Vsevolod Alekseevich Solonnikov. Denisova, I.; Ladyzhenskaya, O.; Seregin, G.; Uraltseva, N.; Frolova, E. // Journal of Mathematical Sciences;Oct2005, Vol. 130 Issue 4, p4775 

    Bibliography: 42 titles.

  • A Mixed Problem for a Hyperbolic System on the Plane with Delay in the Boundary Conditions. Lyul'ko, N. // Siberian Mathematical Journal;Sep2005, Vol. 46 Issue 5, p879 

    We examine well-posedness of the boundary value problem in a half-strip for a first-order linear hyperbolic system with delay (lumped and distributed) in the boundary conditions. In the case of the negative real parts of the eigenvalues of the corresponding spectral problem we prove a time...

  • Homogenization of the Free Boundary Velocity. Kim, Inwon C. // Archive for Rational Mechanics & Analysis;Jul2007, Vol. 185 Issue 1, p69 

    In this paper we investigate some free boundary problems with space-dependent free boundary velocities. Based on maximum principle-type arguments, we show the uniform convergence of the solutions in the homogenization limit. The main step is to show the uniqueness of the limiting free boundary...

  • CHEBYSHEV WEIGHTED NORM LEAST-SQUARES SPECTRAL METHODS FOR THE ELLIPTIC PROBLEM. Sang Dong Kim; Byeong Chun Shin // Journal of Computational Mathematics;Jul2006, Vol. 24 Issue 4, p451 

    We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw²- and Hw w-1- norm of the residual...

  • Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems. Mukherjee, Kaushik; Natesan, Srinivasan // Computing;Jun2009, Vol. 84 Issue 3/4, p209 

    In this paper, we propose a numerical scheme which is almost second-order spatial accurate for a one-dimensional singularly perturbed parabolic convection-diffusion problem exhibiting a regular boundary layer. The proposed numerical scheme consists of classical backward-Euler method for the time...

  • The pyramidal block element. Babeshko, V. A.; Babeshko, O. M.; Evdokimova, O. V. // Doklady Physics;Sep2009, Vol. 54 Issue 9, p418 

    The article offers information in considering a block element in the form of rectangular parallelepiped through the boundary-value problem as example for the anisotropic equation. The block element can be used to identify the solutions of boundary problems on a plane boundary. Identifying...

  • Effect of Surface Properties on the Shear Wave Parameters. Dudko, V. V.; Yushkanov, A. A.; Yalamov, Yu. I. // Technical Physics;Apr2005, Vol. 50 Issue 4, p526 

    The interaction of a viscous gas with a vibrating surface is studied in terms of the Maxwell boundary conditions with regard to isothermal slip. © 2005 Pleiades Publishing, Inc.

  • Least Supersolution Approach to Regularizing Free Boundary Problems. Moreira, Diego; Brenier, Y. // Archive for Rational Mechanics & Analysis;Jan2009, Vol. 191 Issue 1, p97 

    In this paper, we study a free boundary problem obtained as a limit as ε → 0 to the following regularizing family of semilinear equations $${\Delta u = \beta_{\varepsilon}(u) F(\nabla u)}$$ , where β ε approximates the Dirac delta in the origin and F is a Lipschitz function...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics