"Simple schemes for complex problems" by Malgorzata Peszynska, OSU in STAG 111.

Abstract: ​We present our recent results on numerical schemes for evolution PDE models involving multivalued maximal monotone graphs. The unifying scheme of our work is fully implicit treatment of the nonlinearity and the use of lowest order spatial discretizations appropriate for the low regularity of the solutions typical, e.g., in parabolic variational inequalities and free boundaries. The models we consider are typically part of larger coupled systems, and/or are subject to upscaling, thus stability, robustness, and conservation properties are key. We present some rigorous analyses and illustrate the use of the schemes for micro- and meso (Darcy) scale models arising in environmental studies linked to climate variability. This is joint work with many students and collaborators to be named in the talk.  ​​​​​​