Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems

This work continues a line of on developing partially explicit methods for multiscale problems. In our previous works, we considered linear problems where the spatial heterogeneities are at subgrid level and not resolved. these have introduced contrast-independent, time discretizations equations. The discretization divides space into two components: contrast dependent (fast) independent (slow) spaces defined via decomposition. Following this decomposition, temporal splitting was proposed, which treats fast components implicitly slow explicitly. decomposition chosen such that they guarantees stability, formulated condition stepping. as spaces. paper, extend approach to nonlinear We propose derive stability. requires some type contrast-independent solution. present numerical results show proposed provide similar implicit with step is contrast.