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Galerkin's finite element formulation of the system of fourth‐order boundary‐value problems
Author(s) -
Iqbal Shaukat
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20595
Subject(s) - mathematics , cubic hermite spline , spline interpolation , hermite interpolation , monotone cubic interpolation , hermite spline , galerkin method , finite element method , boundary value problem , spline (mechanical) , smoothing spline , hermite polynomials , thin plate spline , interpolation (computer graphics) , method of mean weighted residuals , mathematical analysis , superconvergence , b spline , discontinuous galerkin method , polynomial , polynomial interpolation , linear interpolation , computer graphics (images) , bilinear interpolation , structural engineering , computer science , engineering , thermodynamics , animation , statistics , physics
In this article, a Galerkin's finite element approach based on weighted‐residual is presented to find approximate solutions of a system of fourth‐order boundary‐value problems associated with obstacle, unilateral and contact problems. The approach utilizes a piece‐wise cubic approximations utilizing cubic Hermite interpolation polynomials. Numerical studies have shown the superior accuracy and lesser computational cost of the scheme in comparison to cubic spline, non‐polynomial spline and cubic non‐polynomial spline methods. Numerical examples are presented to illustrate the applicability of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1551–1560, 2011