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Wavelet Methods for Elliptic Partial Differential Equations$
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Karsten Urban

Print publication date: 2008

Print ISBN-13: 9780198526056

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780198526056.001.0001

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Some Applications

Some Applications

(p.394) 9 Some Applications
Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Oxford University Press

Some recent applications of wavelet methods are shown. The chapter starts with the numerical realization of the WEM and consider the L-shaped domain as a model for a non-separable domain. The chapter tests adaptive wavelet schemes. Next, more complicated domains are considered. In particular, the role of the mapping and matching approach is investigated. Saddle point problems can be seen as a system of equations that are indefinite. It is shown that an adaptive scheme makes usual compatibility constraints void (Ladyshenskaja-Babushka-Brezzi condition). As a particular example, the chapter considers the Stokes problem from Fluid Dynamics.

Keywords:   Wavelet Element Method, saddle point problem, stokes problem, Ladyshenskaja-Babushka-Brezzi condition, inf-sup condition, velocity, pressure

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