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DDC: 510 × Subject: discontinuous Galerkin method ×

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    Adaptive time step control for higher order variational time discretizations applied to convection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Ahmed, Naveed; John, Volker
    Higher order variational time stepping schemes allow an efficient post-processing for computing a higher order solution. This paper presents an adaptive algorithm whose time step control utilizes the post-processed solution. The algorithm is applied to convection-dominated convection-diffusion equations. It is shown that the length of the time step properly reflects the dynamics of the solution. The numerical costs of the adaptive algorithm are discussed.
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    Higher order continuous Galerkin-Petrov time stepping schemes for transient convection-diffusion-reaction equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Ahmed, Naveed; Matties, Gunar
    We present the analysis for the higher order continuous Galerkin-Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a-priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin-Petrov and discontinuous Galerkin time discretization schemes will be given.
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    Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Ahmed, Naveed; Becher, Simon; Matthies, Gunar
    We introduce and analyze discontinuous Galerkin time discretizations coupled with continuous finite element methods based on equal-order interpolation in space for velocity and pressure in transient Stokes problems. Spatial stability of the pressure is ensured by adding a stabilization term based on local projection. We present error estimates for the semi-discrete problem after discretization in space only and for the fully discrete problem. The fully discrete pressure shows an instability in the limit of small time step length. Numerical tests are presented which confirm our theoretical results including the pressure instability.