On Optimal Bilinear Quadrilateral Meshes

D' ; Azevedo, E

Oak Ridge National Laboratory

关键词: Transformations;    Metrics;    Interpolation;    Design;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;   

DOI  :  10.2172/814808
RP-ID  :  ORNL/TM-13688
RP-ID  :  AC05-00OR22725
RP-ID  :  814808

美国|英语

来源: UNT Digital Library

【 摘 要 】

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 ''superconvergent'' 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 corner or point singularities.