Identification of the Coefficient in Elliptic Equations

Diffusion Coefficients Estimation for Elliptic Partial Differential Equations

“…[6,1,19,16,15] and the references therein. Parameter estimation/identification for elliptic partial differential equations and their numerical recovery from the (partial) knowledge of u a is an extensively studied subject that has been formulated in several settings.…”

On the inverse problem of identifying Lamé coefficients in linear elasticity

“…augmented with suitable boundary conditions (see [14][15][16] and the references therein). Our work has been heavily influenced by papers by Knowles [17] and Zou [18], particularly the latter.…”

Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem

“…Recently, we [18] followed Zou [41] and Knowles [28] in using the so-called convex energy functionals instead of least squares ones, and then applied Tikhonov regularization to our one-coefficient estimation problems. 1 We got convergence rates of this approach under very simple source conditions without assuming the "small enough condition" which is popular in the theory of nonlinear ill-posed problems (see e.g. [14]).…”

“…We note that in our setting we assume to have observations of z δ ∈ L 2 ( ), ∇z δ ∈ (L 2 ( )) d for the solution u and its gradient, respectively. Such assumptions have been used by many authors, e.g., Acar [1], Banks and Kunisch [4], Chan and Tai [7,8], Chavent [9], Chavent and Kunisch [10], Chen and Zou [11], Ito and Kunisch [20,21], Ito, Kroller and Kunisch [23], Keung and Zou [25], Knowles et al [28,29], Kohn and Lowe [31], Vainikko [37,38], Vainikko and Kunisch [39], Zou [41]. In practice, the observation is measured at certain points and we need to interpolate the point observations to get distributed observations.…”