Related papers: Iterative Methods for an Inverse Eddy Current Prob…
This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint…
In this paper we investigate the non-linear and ill-posed inverse problem of simultaneously identifying the conductivity and the reaction in diffuse optical tomography with noisy measurement data available on an accessible part of the…
In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…
We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the…
We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function.…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of Frequency Domain Electromagnetic…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of…