48 or 749 are transformed to the canonical element and

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Unformatted text preview: x superconvergence which implies that the solution at vertices converges more rapidly than it does globally. Vertex superconvergence has been rigorously established in certain circumstances (e.g., for uniform meshes of square elements), but it seems to hold more widely than current theory would suggest. In the present context, vertex superconvergence implies that the bilinear vertex solution c1 , i j = 1 2, converges at a higher rate ij than the solution elsewhere on Element e. Thus, the error at the vertices c2 , i j = 1 2, ij may be neglected relative to d23 , i = 1 2, and d2j , j = 1 2. With this simpli cation, i 3 7.4. A Posteriori Error Estimation 23 (7.4.13) becomes E( )= 2 X i=1 dN( 2 i3 )+ 2 i3 2 X j =1 d2j N32j ( 3 ): (7.4.14) Thus, there are four unknowns d2 , d2 , d2 , and d2 per element. This technique may be 13 23 31 32 N contains complete polynomials of degree p, S N only ~ carried to higher orders. Thus, if SE contains the hierarchical correction of order p + 1. All lower-order terms are neglected in the error e...
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