Error Estimation for Model-Order Reduction of Finite-Element Parametric Problems

To solve a parametric model in computational electromagnetics, the finite-element (FE) method is often used. To reduce the computational time and the memory requirement, the FE method can be combined with the model-order reduction technique like the proper orthogonal decomposition and (discrete) empirical interpolation methods. These three numerical methods introduce the errors of discretization, reduction, and interpolation, respectively. The solution of the parametric model will be efficient if the three errors are of the same order and so they need to be evaluated and compared. In this paper, we propose an a posteriori error estimator based on the verification of the constitutive law, which estimates the three different errors. An example of application in magnetostatics with 11 parameters is treated where it is shown how the error estimator can be used to control and to improve the accuracy of the solution of the reduced model.