Optimal approximation spaces for problems with rough coefficients
For more information about this meeting, contact Yuxi Zheng.
Speaker: Helen Li, University of Maryland
Abstract: This talk concerns the approximate solution of 2m-th order elliptic equations with rough coefficients, such as arise in the study of heterogeneous materials. Since it is known that the usual finite element method, which employs piecewise polynomial shape functions, does not provide accurate approximation for such problems, we use ^special shape functions^ which reflect the local nature of the unknown solution more accurately than do piecewise polynomials. These shape functions are solutions of the related homogeneous equation, and can be viewed as a generalization of classical L-splines. I will also address the problem of identifying optimal shape functions, and it is shown that the special shape functions are optimal in the sense of N-widths.
Room Reservation Information
Room Number: 216 McAllister
Time: 3:35pm - 4:25pm