Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Two-Sided A Posteriori Error Estimates for Mixed Formulations of Elliptic Problems

Abstract: The present work is devoted to the a posteriori error estimation for mixed approximations of linear self-adjoint elliptic problems. New guaranteed upper and lower bounds for the error measured in the natural product norm are derived, and individual sharp upper bounds are obtained for approximation errors in each of the physical variables. All estimates are reliable and valid for any approximate solution from the class of admissible functions. The estimates contain only global constants depending solely on the domain geometry and the given operators. Moreover, it is shown that, after an appropriate scaling of the coordinates and the equation, the ratio of the upper and lower bounds for the error in the product norm never exceeds 3. The possible methods of finding the approximate mixed solution in the class of admissible functions are discussed. The estimates are computationally very cheap and can also be used for the indication of the local error distribution. As applications, the diffusion problem as well as the problem of linear elasticity are considered.

Confidence region estimation techniques for nonlinear regression in groundwater flow: Three case studies

Abstract: [1] This work focuses on different methods to generate confidence regions for nonlinear parameter identification problems. Three methods for confidence region estimation are considered: a linear approximation method, an F test method, and a log likelihood method. Each of these methods are applied to three case studies. One case study is a problem with synthetic data, and the other two case studies identify hydraulic parameters in groundwater flow problems based on experimental well test results. The confidence regions for each case study are analyzed and compared. Although the F test and log likelihood methods result in similar regions, there are differences between these regions and the regions generated by the linear approximation method for nonlinear problems. The differing results, capabilities, and drawbacks of all three methods are discussed.