Burkardt, J. (2013) Finite Element Treatment of the Navier Stokes Equations, Part IV, Solving the Discretized Navier Stokes Equations. Technical Report, Florida State University, Tallahassee.

has been cited by the following article:

• TITLE: Towards a Micromechanical Understanding of Landslides—Aiming at a Combination of Finite and Discrete Elements with Minimal Number of Degrees of Freedom

  AUTHORS: Jan Mueller, Akira Kyotani, Hans-Georg Matuttis

  KEYWORDS: Finite Element Method, Discrete Element Method, Multi-Phase Flow

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.9, September 14, 2020

  ABSTRACT: In this paper, we propose a combination of discrete elements for the soil and finite elements for the fluid flow field inside the pore space to simulate the triggering of landslides. We give the details for the implementation of third order finite elements (“P2 with bubble”) together with polygonal discrete elements, which allows the formulation with a minimal number of degrees of freedom to save computer time and memory. We verify the implementation with several standard problems from computational fluid dynamics, as well as the decay of a granular step in a fluid as test case for complex flow.