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Unformatted text preview: complexity, FD is often used in time. Finite elements are used, in time, too, but this is much less standard. (in 2D) Meet finite elements (recap) • A few key contrasts between finite elements and finite differences are: – A finite element solution is defined everywhere, not just at certain points • This leads to a much richer theory – A finite element solution can be “weaker” than the continuous solution in the number of derivatives that it possesses • This leads to simplified algebraic and integration formulae – Finite elements can accommodate more general geometry • This makes them easier to generalize beyond simple test cases • For the 1D Laplacian, however, they look much the same! Finite elements Finite elements, cont. Finite elements, cont. x i x i+1 x i1 Φ i (x) Φ i+1 (x) Finite elements, cont. Matrix formulation...
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This note was uploaded on 08/30/2011 for the course APMA 4301 taught by Professor Keyes during the Fall '08 term at Columbia.
 Fall '08
 Keyes

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