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We begin by discussing the finite element approximation of stationary Fokker--Planck--Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients, and one with merely essentially bounded measurable coefficients under a Cordes-type condition. These problems arise as governing equations for the invariant measure in the homogenization of nondivergence-form equations with large drifts. We then suggest and rigorously analyze an approximation scheme for the effective diffusion matrix in both settings, based on the finite element scheme for stationary FPK problems developed in the first part. This is joint work with Endre Süli (University of Oxford) and Zhiwen Zhang (The University of Hong Kong). Bio: Timo Sprekeler is an assistant professor in the Department of Mathematics at Texas A&M University. Dr. Sprekeler completed his Ph.D. at Oxford University under the direction of Endre Süli. He is an expert in multiscale finite element methods, of the homogenization persuasion, and has focused on elliptic problems in nondivergence-form with potentially discontinuous coefficients. Join via Teams Meeting ID: 211 933 286 204 Passcode: 5EH2zt2j Host: Steven Walton, T-5 |