Filters

2014 - 201912020 - 20211

More filters

2019 - 201912020 - 20221
Reset filters

Settings

Has files: Yes × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: algebraic flux correction ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr
    Algebraic flux correction schemes are nonlinear discretizations of convection dominated problems. In this work, a scheme from this class is studied for a steady-state convection-diffusion equation in one dimension. It is proved that this scheme satisfies the discrete maximum principle. Also, as it is a nonlinear scheme, the solvability of the linear subproblems arising in a Picard iteration is studied, where positive and negative results are proved. Furthermore, the non-existence of solutions for the nonlinear scheme is proved by means of counterexamples. Therefore, a modification of the method, which ensures the existence of a solution, is proposed. A weak version of the discrete maximum principle is proved for this modified method.
  • Thumbnail Image
    Item
    An assessment of solvers for algebraically stabilized discretizations of convection-diffusion-reaction equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Jha, Abhinav; Pártl, Ondřej; Ahmed, Naveed; Kuzmin, Dmitri
    We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include flux-corrected transport schemes and monolithic limiters. We discretize in space using a continuous Galerkin method and P1 or Q1 finite elements. Time integration is performed using the Crank-Nicolson method or an explicit strong stability preserving Runge-Kutta method. Nonlinear systems are solved using a fixed-point iteration method, which requires solution of large linear systems at each iteration or time step. The great variety of options in the choice of discretization methods and solver components calls for a dedicated comparative study of existing approaches. To perform such a study, we define new 3D test problems for time dependent and stationary convection-diffusion-reaction equations. The results of our numerical experiments illustrate how the limiting technique, time discretization and solver impact on the overall performance.