6533b839fe1ef96bd12a6dde

RESEARCH PRODUCT

Comparison of continuous and discontinuous Galerkin approaches for variable-viscosity Stokes flow

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We describe a Discontinuous Galerkin (DG) scheme for variable-viscosity Stokes flow which is a crucial aspect of many geophysical modelling applications and conduct numerical experiments with different elements comparing the DG approach to the standard Finite Element Method (FEM). We compare the divergence-conforming lowest-order Raviart-Thomas (RT0P0) and Brezzi-Douglas-Marini (BDM1P0) element in the DG scheme with the bilinear Q1P0 and biquadratic Q2P1 elements for velocity and their matching piecewise constant/linear elements for pressure in the standard continuous Galerkin (CG) scheme with respect to accuracy and memory usage in 2D benchmark setups. We find that for the chosen geodynamic benchmark setups the DG scheme with the BDM1P0 element gives the expected convergence rates and accuracy but has (for fixed mesh) higher memory requirements than the CG scheme with the Q1P0 element without yielding significantly higher accuracy. The DG scheme with the RT0P0 element is cheaper than the other first-order elements and yields almost the same accuracy in simple cases but does not converge for setups with non-zero shear stress. The known instability modes of the Q1P0 element did not play a role in the tested setups leading to the BDM1P0 and Q1P0 elements being equally reliable. Not only for a fixed mesh resolution, but also for fixed memory limitations, using a second-order element like Q2P1 gives higher accuracy than the considered first-order elements.