On Lagrangian schemes for porous medium type generalized diffusion equations: A discrete energetic variational approach

Chun Liu, Yiwei Wang

Research output: Contribution to journalArticle

Abstract

In this paper, we present a systematic framework to derive a variational Lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach. Such discrete energetic variational approaches are analogous to energetic variational approaches [39,25] in a semidiscrete level, which provide a basis of deriving variational “semi-discrete equations” and can be applied to a large class of partial differential equations with energetic variational structures. The numerical schemes derived by this framework can inherit the variational structure from the continuous energy-dissipation law. As an illustration, we develop two variational Lagrangian schemes for the multidimensional porous medium equations (PME), based on two different energy-dissipation laws. We focus on the numerical scheme based on the energy-dissipation law with [Formula presented] as the dissipation functional. Several numerical experiments demonstrate the accuracy of this scheme as well as its ability in capturing the free boundary and estimating the waiting time for the PME in both 1D and 2D.

Original languageEnglish (US)
Article number109566
JournalJournal of Computational Physics
Volume417
DOIs
StatePublished - Sep 15 2020

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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