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Unformatted text preview: seek an error estimation technique that only requires local (element level) mesh
computations, so let's construct a local Galerkin problem on element e by integrating
(7.4.1a) over e and applying the divergence theorem to obtain: determine u 2 H 1( e)
such that Ae(v u) = (v f )e+ < v pun >e
where
(v f )e = ZZ 8v 2 H 1 ( e ) (7.4.4a) vfdxdy (7.4.4b) prv ru + qvu]dxdy (7.4.4c) e Ae(v u) = ZZ
e and < v u >e= Z
@e vuds: (7.4.4d) As usual, e is the domain of element e, s is a coordinate along @ e , and n is a unit
outward normal to @ e .
Let u=U +e (7.4.5) where e(x y) is the discretization error of the nite element solution, and substitute
(7.4.5) into (7.4.4a) to obtain Ae(v e) = (v f )e ; Ae(v U )+ < v pun >e 8v 2 H 1 ( e ): (7.4.6) Equation (7.4.6), of course, cannot be solved because (i) v, u, and e are elements of an
in nitedimensional space and (ii) the ux pun is unknown on @ e . We could obtain
a nite element solution of (7.4.6) by approximating e and v by E and V in a n...
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.
 Spring '14
 JosephE.Flaherty

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