Unformatted text preview: the Fner the mesh necessary to achieve a given accuracy. CHALLENGE 31.3. (a) Suppose (for convenience of notation) that Ω ⊂ R 2 . (Other dimensions are just as easy.) ±irst we apply integration by parts (with zero boundary conditions) to see that if w ± = 0 ( w, A w ) = − Z Z Ω w ∇ · ( a ∇ w )d x d y = Z Z Ω ∇ w · ( a ∇ w )d x d y = Z Z Ω a 1 ( x, y ) µ ∂w ∂x ¶ 2 + a 2 ( x, y ) µ ∂w ∂y ¶ 2 d x d y ≥ ,...
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- Fall '11
- Eigenvalue, eigenvector and eigenspace, eigenvalue approximations, error ratios