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On solenoidal high‐degree polynomial approximations to solutions of the stationary Stokes equations
Author(s) -
Swann Howard
Publication year - 2000
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 - 10.1002/1098-2426(200009)16:5<480::aid-num5>3.0.co;2-u
Subject(s) - mathematics , solenoidal vector field , degree of a polynomial , degree (music) , polynomial , discretization , convergence (economics) , finite element method , mathematical analysis , partial differential equation , approximations of π , approximation error , extension (predicate logic) , geometry , vector field , physics , acoustics , computer science , programming language , economics , thermodynamics , economic growth
The cell discretization algorithm, a nonconforming extension of the finite element method, is used to obtain approximations to the velocity and pressure functions satisfying the Stokes equations. Error estimates show convergence of the method. An implementation using polynomial bases is described that permits the use of the continuous approximations of the h‐p finite element method and exactly satisfies the solenoidal requirement. We express the error estimates in terms of the diameter h of a cell and degree p of the approximation on each cell. Examples of 10 th degree polynomial approximations are described that substantiate the theoretical estimates. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 480–493, 2000