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Unformatted text preview: . We'll pursue some remedies to this problem later
in this section, but, rst, let us look at another application.
Example 7.4.2. Ai a 4] considers the nonlinear parabolic problem
(x y) 2 (0 1) (0 1)
t>0
ut + qu2(u ; 1) = uxx + uyy
2
with the inital and Dirichlet boundary conditions speci ed so that the exact solution is
pq=2(1x+y;tpq=2) :
u(x y t) =
1+e
He estimates the spatial discretization error using the residual estimate (7.4.8) neglecting
~
the error at vertices. The error estimation space S N consists of the hierarchical corrections
of degree p + 1 however, some lowerdegree hierarchical terms are used in some cases.
This is to provide a better equilibration of boundary terms and improve results. although
this is a timedependent problem, which we haven't studied yet, Ai a 4] keeps the
temporal errors small to concentrate on spatial error estimation. With q = 500, Ai a's
4] e ectivity indices in H 1 at t = 0:06 are presented in Table 7.4.1 for computations
performed on uniform mesh...
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 Spring '14
 JosephE.Flaherty

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