در یک راه حل قابل اعتماد از یک معادله بیضی شبه خطی با ضرایب نامشخص: تجزیه و تحلیل حساسیت و نمونه های عددی

The aim of the paper is to add sensitivity analysis and numerical tests to the existence and convergence results published in [2]. The isotropic material case is studied in [1]. By way of contrast, anisotropic medium is considered in this paper. The mathematical problem examined in the paper has a clear physical meaning. In the words of physics, we can say we consider a steady-state heat flow in an anisotropic body. The temperature distribution is modeled by a quasilinear elliptic equation with uncertain coefficients of heat conductivity. These are temperature dependent and belong to an admissible set derived from measurements, for example. We choose a small test subdomain G and look for the difference between the highest and the lowest mean temperature we can get on G taking into account admissible conductivities. Since the body is anisotropic, the Kirchhoff transformation cannot be applied to get rid of the nonlinearity in the state equation. Also, cost functional gradient computation is more complex than in the case of an isotropic material (cf. [1]). The paper is organized as follows. In Section 2, we briefly introduce the problem and its approximation, and give a survey of relevant existence as well as convergence results. Section 3 deals with sensitivity analysis, i.e., we focus on the gradient of the cost functional. Finally, numerical examples are presented in Section 4.