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Hermite infinite elements and graded quadratic B‐spline finite elements
Author(s) -
Gardner L. R. T.,
Gardner G. A.,
Dag I.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361908
Subject(s) - hermite polynomials , finite element method , mathematics , quadratic equation , mathematical analysis , b spline , spline (mechanical) , mixed finite element method , hermite spline , extended finite element method , boundary value problem , geometry , thin plate spline , physics , spline interpolation , thermodynamics , statistics , bilinear interpolation
Quadratic B‐spline finite elements are defined for a graded mesh. Hermite infinite elements are proposed to extend the applicability of these finite elements to unbounded regions. Test problems used to compare this technique with published procedures show that the quadratic B‐spline finite element solution has, as expected, lower error bounds than a linear element solution. These experiments also demonstrate that the Hermite infinite elements used to close the B‐spline finite element arrays lead to error norms comparable in size with other infinite element formulations. The generation of solitary waves in a semi‐infinite shallow channel by boundary forcing is modelled by the Korteweg‐de Vries equation using an array of graded elements closed by a zero pole infinite element. The resulting simulation of solitary wave motion across a non‐uniform mesh confirms existing work and illustrates the effectiveness of the present formulation.