UNCERTAINTY QUANTIFICATION AND WEAK APPROXIMATION OF AN ELLIPTIC INVERSE PROBLEM

We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation in divergence form, in a bounded domain in dime...

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Bibliographic Details
Published in:	SIAM journal on numerical analysis Vol. 49; no. 5/6; pp. 2524 - 2542
Main Authors:	DASHTI, M., STUART, A. M.
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:	Approximation Banach space Banach spaces Covariance Diffusion coefficient Elliptic differential equations Exact sciences and technology Inverse problems Mathematical analysis Mathematical functions Mathematical theorems Mathematics Numerical analysis Numerical analysis in abstract spaces Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Permeability Quantification Random variables Sciences and techniques of general use Truncation uncertainty quantification Approximation Error estimation Initial value problem Well posed problem Banach space Partial differential equation Inverse problem Truncation 35J99 Weak convergence Bayesian approach elliptic inverse problem Numerical analysis Porous medium flow Elliptic equation Boundary value problem Linear equation inverse problems Lipschitz function 62G99
ISSN:	0036-1429, 1095-7170
Online Access:	Get full text
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