Numerical analysis of elliptic inverse problems with interior data

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Interior Penalty Discontinuous Approximations of Elliptic Problems

This paper studies an interior penalty discontinuous approximation of elliptic problems on non–matching grids. Error analysis, interface domain decomposition type preconditioners, as well as numerical results illustrating both, discretization errors and condition number estimates of the problem and reduced forms of it, are presented.

Data-sparse Approximate Inverse in Elliptic Problems: Green’s Function Approach

A Globally Convergent Numerical Method for Some Coefficient Inverse Problems with Resulting Second Order Elliptic Equations

A new globally convergent numerical method is developed for some multidimensional Coefficient Inverse Problems for hyperbolic and parabolic PDEs with applications in acoustics, electromagnetics and optical medical imaging. On each iterative step the Dirichlet boundary value problem for a second order elliptic equation is solved. The global convergence is rigorously proven and numerical experime...

Measure Data and Numerical Schemes for Elliptic Problems

In order to show existence of solutions for linear elliptic problems with measure data, a first classical method, due to Stampacchia, is to use a duality argument (and a regularity result for elliptic problems). Another classical method is to pass to the limit on approximate solutions obtained with regular data (converging towards the measure data). A third method is presented. It consists to p...