FINITE ELEMENT ERROR ANALYSIS OF A MANTLE CONVECTION MODEL

John V., KAYA MERDAN S., Novo J.

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, vol.15, pp.677-698, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 15
  • Publication Date: 2018
  • Journal Name: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.677-698
  • Keywords: Mantel Convection, Stokes problem with variable viscosity, temperature problem with variable thermal convection, inf-sup stable finite elements, SUPG stabilization, DIFFUSION-REACTION EQUATIONS, TEMPERATURE-DEPENDENT COEFFICIENTS, INFINITE PRANDTL NUMBER, VARIABLE VISCOSITY, SPHERICAL-SHELL, STABILIZATION, DIVERGENCE, ALGORITHM
  • Middle East Technical University Affiliated: Yes

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.