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On Optimal Bilinear Quadrilateral Meshes

D'Azevedo, Ed

Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.19-33, October 1998


7th International Meshing Roundtable
October 26-28, 1998
Dearborn, Michigan, USA

Computer Science and Mathematics Division,
Oak Ridge National Laboratory,
P.O. Box 2008. Oak Ridge, TN 37831-6367

The novelty of this work is in presenting interesting error properties of two types of asymptotically "optimal" quadrilateral meshes for bilinear approximation. The first type of mesh has an error equidistributing property where the maximum interpolation error is asymptotically the same over all elements. The second type has faster than expected "super-convergence" property for certain saddle-shaped data functions. The "super-convergent" mesh may be an order of magnitude more accurate than the error equidistributing mesh. Both types of mesh are generated by a coordinate transformation of a regular mesh of squares. The coordinate transformation is derived by interpreting the Hessian matrix of a data function as a metric tensor. The insights in this work may have application in mesh design near known corner or point singularities.

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