Abstract.
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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D’Azevedo, E. On Optimal Bilinear Quadrilateral Meshes. Engineering with Computers 15, 219–227 (1999). https://doi.org/10.1007/s003660050017
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DOI: https://doi.org/10.1007/s003660050017