Learn More
When estimating hydraulic transmissivity the question of parameterization is of great importance. The transmissivity is assumed to be a piecewise constant space dependent function and the unknowns are both the transmissivity values and the zonation, the partition of the domain whose parts correspond to the zones where the transmissivity is constant.(More)
1 Problem statement and functions of bounded variation We consider the problem of nding approximate solutions to Tu = z (1.1) where T is a bounded linear operator from L 2 (() to a Hilbert space Y by using regularization techniques based on bounded variation functionals. Here is a bounded domain in IR n with Lipschitzian boundary and z 2 Y. The operator T(More)
We consider the problem of determining the diffusion coefficient a(x) in a 2D elliptic equation from a distributed measurement z in H 1 of the solution u of the equation. For a problem with a simple geometry, we give conditions under which the first derivative of the b = 1=a 7 ;! u mapping is coercive. Then we show that its non linearity in a direction d(More)
We introduce a new global pressure formulation for immiscible three-phase compressible flows in porous media which is fully equivalent to the original equations, unlike the one introduced in [5]. In this formulation, the total volumetric flow of the three fluids and the global pressure follow a classical Darcy law, which simplifies the resolution of the(More)
A new method for formulating and solving parameter estimation problems based on Fenchel duality is presented. The partial diierential equation is considered as a contraint in a least squares type formulation and is realized as a penalty term involving the primal and dual energy functionals associated with the diierential equation. Splitting algorithms and(More)
The estimation of distributed parameters in a partial differential equation (PDE) from measures of the solution of the PDE may lead to underdetermination problems. The choice of a parameterization is a frequently used way of adding a priori information by reducing the number of unknowns according to the physics of the problem. The refinement indicators(More)