Error analysis of a discontinuous Galerkin method for degenerate parabolic equations

• Date: 14. 12. 2023
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Sunčica Sakić

In this talk, we present an error analysis for the spatial discretization of Richards’ equation, which is widely used in porous media flow modeling. Richards’ equation is a doubly nonlinear parabolic partial differential equation that can degenerate into an elliptic or ordinary differential equation. Therefore, it is challenging to develop and analyze a sufficiently accurate and efficient method for its numerical solution. We transform the original problem using an expanded mixed formulation and define the local discontinuous Galerkin method to discretize the spatial variable while the temporal variable remains continuous. We derive error estimates in terms of the Holder coefficient of nonlinear temporal derivative function and spatial discretization parameter. Moreover, we support the theoretical results by numerical experiments.