20150706
Traditionally in the geodynamics community, staggered grid finite difference schemes and mixed Finite Elements (FE) have been utilised to discretize the variable viscosity Stokes problem. While these methods are considered to be sufficiently robust and accurate for a wide range of variable viscosity problems they tend to have infsup constants which are highly dependent on the cell aspect ratio. Discontinuous Galerkin (DG) methods alleviate this issue, which motivates their investigation in the context of geodynamics, where they did not receive much attention so far.
Specifically, we rigorously evaluate the applicability of two Interior Penalty Discontinuous Galerkin methods, namely the Nonsymmetric and Symmetric Interior Penalty Galerkin methods (NIPG and SIPG) for compressible elasticity and incompressible, variable viscosity Stokes problems. Numerical evidence is presented that the NIPG scheme is stable and convergent for \(P_k\) spaces even in the incompressible limit on conforming quadrilateral meshes. Both formulations are investigated for their convergence properties regarding velocity and pressure in the context of the Stokes problem. Numerical tests indicate that no spurious features emerge in either the pressure or velocity field.
In order to consider geodynamical applications the timedependency of the mantle and lithosphere composition is taken into account through an auxiliary advection equation. Realistic simulations require computing on large clusters and the application of robust and scalable preconditioners, which will also be addressed.
Category: CE SeminarTechnische Universität Darmstadt
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