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Title: Anisotropic piecewise linear approximation
Author: Rabarison, Andrianarivo Fabien
ISNI:       0000 0004 2743 5020
Awarding Body: University of Strathclyde
Current Institution: University of Strathclyde
Date of Award: 2012
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The subject of this thesis includes the design of new partitioning methods for the approximation of a function f on a domain C Rd, d 2, by piecewise linear functions, and the derivation of errors estimations in Lp-norm and W1 p - seminorm. In the two-dimensional setting, we develop a construction of a sequence of anisotropic triangulations, where the approximation provided by the piecewise linear interpolant for a given f C2() with a positive definite Hessian, is asymptotically optimal in Lp-norm and in the same time optimal in W1 p - seminorm with respect to the number of degrees of freedom. As a preparation for this result, we review various local error bounds for the interpolation by linear polynomials on a triangle, and derive a number of new estimates of this type. In addition, for functions of d 2 variables, we propose a new approximation method, where several overlaying partitions of are designed such that the sum of piecewise constant or piecewise linear polynomials over these partitions provides a better approximation order than the one obtainable by using a single partition.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available