Work

A fully implicit second order method for viscous free surface Stokes flow – application to glacier simulations

Year: 2026

Type: article

Abstract: . We present a fully implicit finite element method for viscous free surface Stokes problems which are common in glaciology and geodynamics. Standard fully implicit iterative solvers diverge for such problems when using large time steps. We address this by incorporating a stabilization term that vanishes upon convergence. This approach enables the use of large time steps, thereby significantly improving the efficiency of simulations. Furthermore, we leverage the fully implicit solver to develop second-order time-stepping schemes that mitigate the high errors associated with first-order methods for large time steps. The methods are tested and evaluated on model domains relevant to geodynamics and glaciology.

Source: Geoscientific model development

DOI: 10.5194/gmd-19-2333-2026

Authors: Josefin Ahlkrona, A. Clara J. Henry, André Löfgren

Institutions: Stockholm University, Swedish e-Science Research Centre, Bolin Centre for Climate Research

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,725

Funders: Swedish e-Science Research Centre, Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet