This solution is singular since ur r12 near the

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Unformatted text preview: ar and quadratic polynomials were used as nite element bases. Local e ectivity indices on L and R are not close to unity and don't appear to be converging as either the mesh spacing is re ned or p is increased. Global e ectivity indices are near unity. Convergence to unity is di cult to appraise with the limited data. 30 Analysis of the Finite Element Method At this time, the eld of a posteriori error estimation is still emerging. Error estimates for problems with singularities are not generally available. The performance of error estimates is dependent on both the problem, the mesh, and the basis. Error estimates for realistic nonlinear and transient problems are just emerging. Verfurth 20] provides an exceelent survey of methods and results. Bibliography 1] S. Adjerid, B. Belguendouz, and J.E. Flaherty. A posteriori nite element error estimation for di usion problems. Technical Report 9-1996, Scienti c Computation Research Center, Rensselaer Polytechnic Institute, Troy, 1996. SIAM Journal on Scienti c Computation, to appear. 2] S....
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