43 e ectivity indices for several error estimation

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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 lower-degree hierarchical terms are used in some cases. This is to provide a better equilibration of boundary terms and improve results. although this is a time-dependent 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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