Robust Model Reduction for High-contrast Problems

Major progress has been made recently to make preconditioners robust with respect to variation of coefficients. A reason for this success is the adaptive selection of primal constraints based on localized generalized eigenvalue problems. In this talk we discuss how to transfer this technique to the field of discretizations. Given a target accuracy, we design a robust model reduction by delocalizing multiscale basis functions and establish a priori energy error estimates with such target accuracy with hidden constants independently of the coefficients. This is a joint work with Alexandre Madureira from LNCC, Brazil.