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A new class of stabilized mesh‐free finite elements for the approximation of the Stokes problem
Author(s) -
Srinivas Kumar V. V. K.,
Rathish Kumar B. V.,
Das P. C.
Publication year - 2004
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.20007
Subject(s) - mathematics , quadrilateral , finite element method , mathematical analysis , constant (computer programming) , constant coefficients , quadratic equation , stokes flow , spline (mechanical) , domain (mathematical analysis) , geometry , physics , engineering , thermodynamics , programming language , flow (mathematics) , structural engineering , computer science
Previously, we solved the Stokes problem using a new linear ‐ constant stabilized mesh‐free finite element based on linear Weighted Extended B ‐ splines (WEB‐splines) as shape functions for the velocity approximation and constant extended B‐splines for the pressure (Kumar et al., 2002). In this article we derive another linear‐constant element that uses the Haar wavelets for the pressure approximation and a quadratic ‐ linear element that uses quadrilateral bubble functions for the enrichment of the velocity approximation space. The inf‐sup condition or Ladyshenskaya‐Babus̆ka‐Brezzi (LBB) condition is verified for both the elements. The main advantage of these new elements over standard finite elements is that they use regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre‐processing step. Convergence and condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.