A collage-based approach to inverse problems for non-linear elliptic PDEs. (1st January 2012)

• Record Type: Journal Article
• Authors: Levere, Kim M.
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 3:Number 4(2012)
• Page Start: 281
• Page End: 297
• Publication Date: 2012-01-01
• Subjects: collage coding -- fractal-based methods -- inverse problems -- parameter estimation -- partial differential equations -- variational methods -- nonlinear Lax-Milgram representation theorem -- optimisation -- applied analysis -- numerical analysis; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

Abstract

The collage coding solution strategy for ODE inverse problems, first developed in Kunze and Vrscay (1999), controls the approximation error by bounding it above by a more readily minimisable distance. In this paper, we explore a collage coding technique for solving inverse problems for a general class of second-order non-linear elliptic PDEs. The method is based on the nonlinear Lax-Milgram representation theorem and elements of variational calculus. We develop this method for a broad class of non-linear elliptic PDEs and present an example of the method in practice.