Equal-order finite element approximation for mantle-melt transport

Malte Braack*, Kamel Nafa, Simon Taylor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Mantle convection and melt migration are important processes for understanding Earth’s dynamics and how they relate to observations at the surface. Recently it has been established that melt migration can be modelled by coupling variable-viscosity Stokes flow and Darcy flow, where Stokes flow generally captures the long-term behaviour of the mantle and lithosphere, and Darcy flow models the two-phase regime. It is known that approximating the solution by finite element methods requires the use of mixed inf-sup stable elements or additional stabilization terms. Here, we propose a formulation with a coercive non-symmetric linear operator which allows the use of simple equal-order elements.

Original languageEnglish
Pages (from-to)273-293
Number of pages21
JournalJournal of Applied Mathematics and Computing
Volume65
Issue number1-2
DOIs
Publication statusPublished - Feb 2021
Externally publishedYes

Keywords

  • Elliptic differential equations
  • Error estimates
  • Finite elements
  • Porous media

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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