On Optimal Bilinear Quadrilateral Meshes

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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 ... continued below

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15 pages

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D'Azevedo, E. October 26, 1998.

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Description

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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15 pages

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OSTI as DE00771538

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  • 7th International Meshing Roundtable, Dearborn, MI (US), 10/26/1998--10/28/1998

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  • Report No.: P00-105907
  • Grant Number: AC05-00OR22725
  • Office of Scientific & Technical Information Report Number: 771538
  • Archival Resource Key: ark:/67531/metadc722680

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  • October 26, 1998

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  • Sept. 29, 2015, 5:31 a.m.

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  • Jan. 19, 2016, 8:44 p.m.

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D'Azevedo, E. On Optimal Bilinear Quadrilateral Meshes, article, October 26, 1998; Tennessee. (digital.library.unt.edu/ark:/67531/metadc722680/: accessed August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.