Anisotropic piecewise linear approximation

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral-pg

Grantor dc:publisher.institution

University of Strathclyde

Year dc:date.issued

2012

Author dc:creator

• Rabarison, Andrianarivo Fabien

DOI

10.48730/tkrb-hq53

Identifier

T13399

OAI identifier oai:identifier

oai:strathclyde:z029p4825