Investigations into the applicability of adaptive finite element methods to two‐dimensional infinite Prandtl number thermal and thermochemical convection

Abstract

An adaptive finite element procedure is presented for improving the quality of solutions to convection‐dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well‐known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation‐based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well‐established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid‐based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.