Finite Element Error Analysis of a Mantle Convection Model

Authors

  • Volker John Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany and Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
  • Songul Kaya Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey
  • Julia Novo Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain

Keywords:

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

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.

Downloads

Published

2018-08-15

Issue

Vol. 15 No. 4-5 (2018)

Section

Articles