ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
Theoretical error bounds of the form are often available for finite element solutions U of elliptic problems. In this form the estimates give the order of convergence of the method but are of little practical value for estimating the size of the error because the magnitudes of the constant K and the theoretical solution u are unknown. An exception occurs in the case of the equation ∂2u/∂x2 + ∂2u/∂y2 + f = 0 in a rectangle where the Ritz-Galerkin finite element solution involves piecewise linears over a regular triangular grid. In this case where α = 1 and Barnhill and Gregory1 have obtained the theoretical value 0·93√2 for K. In this note calculations are carried out for a variety of problems and the quantity K* = ∥u - U∥E/h∥f∥L2 measured and compared with K. The values of K* obtained fit into a well defined pattern from which we conclude that the theoretical constant K is of the correct order of magnitude.
Additional Material:
1 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620110315
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