WIAS Preprint No. 2403, (2017)

Finite element error analysis of a mantle convection model



Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Kaya, Songul
  • Novo, Julia

2010 Mathematics Subject Classification

  • 65M60 65N30

Keywords

  • Mantel convection, Stokes problem with variable viscosity, temperature problem, with variable thermal convection, inf-sup stable finite elements, SUPG stabilization

DOI

10.20347/WIAS.PREPRINT.2403

Abstract

A mantle convection model consisting of the stationary Stokes equations and a time-dependent convection-diffusion equation for the temperature is studied. The Stokes problem is discretized with a conforming inf-sup stable pair of finite element spaces and the temperature equation is stabilized with the SUPG method. Finite element error estimates are derived which show the dependency of the error of the solution of one problem on the error of the solution of the other equation. The dependency of the error bounds on the coefficients of the problem is monitored.

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