TWO-SCALE FINITE ELEMENT DISCRETIZATIONSFOR INTEGRODIFFERENTIAL EQUATIONS

摘要

In this paper we propose and analyze a num-ber of two-scale discretization schemes for integrodifferential equations arising in finance. It is shown theoretically and numerically that the number of degrees of freedom of the two-scale discretization is significantly smaller than that of the standard one-scale finite element approach while at the same time preserving the accuracy of the one-scale discretization. The main idea of these algorithms is to use a coarse grid to approximate the low frequencies and then to use a fine grid to correct the relatively high frequencies. As a result, both the computational time and the storage can be reduced con-siderably. A combination of wavelet and Lagrangian finite element basis functions is applied to further reduce the com-plexity arising from the non-locality of the integrodifferential operators.