Adaptive Finite Element Methods in Geodynamics; Convection Dominated Mid–Ocean Ridge and Subduction Zone Simulations

Purpose: An adaptive finite element procedure is presented for improving the quality of convection dominated mid–ocean ridge and subduction zone problems in geodynamics. Approach: The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach utilizes an automatic, unstructured mesh generator and a finite element flow solver. Mesh adaptation is accomplished through mesh regeneration, employing information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. Findings: The proposed methodology works remarkably well at improving solution accuracy for both mid–ocean ridge and subduction zone simulations. Furthermore, the method is computationally highly efficient. Originality of paper: To date, successful goal–orientated/error–guided grid adaptation techniques have, to our knowledge, not been utilized within the field of geodynamics. This paper presents the first true geodynamical application of such methods.