Advection-Diffusion Problems on Polygonal Meshes

Watch a technical webinar where Todd Arbogast from the University of Texas at Austin presents a comprehensive framework for solving second-order advection-diffusion PDEs on polygonal computational meshes. Learn about high-order finite element and finite volume techniques that address accuracy challenges on polygons through the introduction of new finite elements with minimal degrees of freedom for Sobolev space conformity. Explore direct serendipity elements for approximating scalar functions like pressures and concentrations, as well as direct mixed elements for handling vector functions such as velocities. Discover solutions for managing shocks and steep fronts in advective problems through finite volume weighted essentially non-oscillatory (WENO) techniques and a multilevel WENO reconstruction with adaptive order. Examine how this approach combines stencil polynomials by down-weighting oscillatory or low-degree polynomials to select smooth, accurate solutions. Study practical applications in three dimensions, including examples in tracer flow and the Richards equation, followed by an interactive Q&A session.