Uploaded November 2024 | Updated September 2026, 1 week ago
Watch our latest webinar series, Advection-Diffusion Problems on Polygonal Meshes, organized by the SIAM Activity Group on Geosciences: siam.org/membership/activity-groups/detail/geosciences.
In this video, Todd Arbogast from the University of Texas at Austin discusses a framework for solving second-order advection-diffusion PDEs on polygonal computational meshes. This framework includes both high-order finite element and finite volume techniques, addressing challenges of maintaining accuracy on polygons by introducing new finite elements with minimal degrees of freedom to ensure Sobolev space conformity.
The direct serendipity elements approximate scalar functions like pressures and concentrations, while direct mixed elements handle vector functions, such as velocities. To address shocks or steep fronts in advective problems, the presentation explores finite volume weighted essentially non-oscillatory (WENO) techniques and introduces a multilevel WENO reconstruction with adaptive order. This approach combines stencil polynomials, selecting smooth, accurate ones by down-weighting oscillatory or low-degree polynomials. Applications to three dimensions are also covered, with examples in tracer flow and the Richards equation.
0:00 Introduction
2:16 Webinar
55:00 Q&A
#webinarseries #geophysics #seismic #environmentalscience #geosciences #dataanalysis #appliedmathematics #renewableenergy #climatechange
Watch our latest webinar series, Advection-Diffusion Problems on Polygonal Meshes, organized by the SIAM Activity Group on Geosciences: siam.org/membership/activity-groups/detail/geosciences.
In this video, Todd Arbogast from the University of Texas at Austin discusses a framework for solving second-order advection-diffusion PDEs on polygonal computational meshes. This framework includes both high-order finite element and finite volume techniques, addressing challenges of maintaining accuracy on polygons by introducing new finite elements with minimal degrees of freedom to ensure Sobolev space conformity.
The direct serendipity elements approximate scalar functions like pressures and concentrations, while direct mixed elements handle vector functions, such as velocities. To address shocks or steep fronts in advective problems, the presentation explores finite volume weighted essentially non-oscillatory (WENO) techniques and introduces a multilevel WENO reconstruction with adaptive order. This approach combines stencil polynomials, selecting smooth, accurate ones by down-weighting oscillatory or low-degree polynomials. Applications to three dimensions are also covered, with examples in tracer flow and the Richards equation.
0:00 Introduction
2:16 Webinar
55:00 Q&A
#webinarseries #geophysics #seismic #environmentalscience #geosciences #dataanalysis #appliedmathematics #renewableenergy #climatechange
