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Volume 15, Issue 4-5
Finite Element Error Analysis of a Mantle Convection Model

Volker John, Songul Kaya & Julia Novo

Int. J. Numer. Anal. Mod., 15 (2018), pp. 677-698.

Published online: 2018-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M60, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

john@wias-berlin.de (Volker John)

smerdan@metu.edu.tr (Songul Kaya)

julia.novo@uam.es (Julia Novo)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-677, author = {John , VolkerKaya , Songul and Novo , Julia}, title = {Finite Element Error Analysis of a Mantle Convection Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {677--698}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12537.html} }
TY - JOUR T1 - Finite Element Error Analysis of a Mantle Convection Model AU - John , Volker AU - Kaya , Songul AU - Novo , Julia JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 677 EP - 698 PY - 2018 DA - 2018/04 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12537.html KW - Mantel Convection, Stokes problem with variable viscosity, temperature problem with variable thermal convection, inf-sup stable finite elements, SUPG stabilization. AB -

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.

Volker John, Songul Kaya & Julia Novo. (2020). Finite Element Error Analysis of a Mantle Convection Model. International Journal of Numerical Analysis and Modeling. 15 (4-5). 677-698. doi:
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