Approximate the solution to the partial differential equation 2u x2 (x, y) + 2u y2 (x
Chapter 12, Problem 3(choose chapter or problem)
Approximate the solution to the partial differential equation 2u x2 (x, y) + 2u y2 (x, y) 12.52 u(x, y) = 252 sin 5 2 x sin 5 2 y, 0 < x, y < 0.4, subject to the Dirichlet boundary condition u(x, y) = 0, using the Finite-Element Algorithm 12.5 with the elements given in the accompanying figure. Compare the approximate solution to the actual solution, u(x, y) = sin 5 2 x sin 5 2 y, at the interior vertices and at the points (0.125, 0.125), (0.125, 0.25), (0.25, 0.125), and (0.25, 0.25). 0.4 0.3 0.2 0.1 0.30.20.1 0.4
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