Abstract Numerical glacier and ice-sheet models compute evolving ice geometry velocity fields using various stress-balance approximations boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these usually require time steps shorter than climate-coupling scales because they update thickness after each solution. High-resolution per...

A fully-implicit numerical method based upon adaptively refined meshes for the thermal-solutal simulation of alloy solidification in 2D is presented. In addition we combine an unconditional stable second-order fully-implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method, where a robust and fast multigrid solver for systems ...

In this paper, we extend our work for the heat equation [1] and for the Stokes equations [2] to the nonstationary Navier-Stokes equations. We present fully implicit continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time stepping schemes for incompressible flow problems which are, in contrast to standard approaches like for instance the Crank-Nicolson scheme, of higher order in ti...

This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time discretization methods is studied numerically with regards to computational efficiency, order of accuracy, and stability, as well as the ability to treat effectively ...

A new approach is proposed for constructing a fully explicit third-order mass-conservative semi-Lagrangian scheme for simulating the shallow-water equations on an equiangular cubed-sphere grid. State variables are staggered with velocity components stored pointwise at nodal points and mass variables stored as element averages. In order to advance the state variables in time, we first apply an e...

We consider time-dependent flow problems discretized with higher order finite element methods. Applying a fully implicit time discretization or an IMEX scheme leads to a saddle point system. This linear system is solved using a preconditioned Krylov method, which is fully parallelized on a distributed memory parallel computer. We study a robust block-triangular preconditioner and beside numeric...

In this paper a combination of discontinuous, piecewise linear, finite elements with implicitexplicit time stepping is considered for convection-reaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadrature rules on accuracy and stability for one-dimensional problems. 2000 Mathematics Subject Classificat...