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Author: Knobloch, Petr × Has files: Yes × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: error analysis × WGL Institute: WIAS ×

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    Finite element pressure stabilizations for incompressible flow problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) John, Volker; Knobloch, Petr; Wilbrandt, Ulrich
    Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis.
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    A unified analysis of Algebraic Flux Correction schemes for convection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr; Rankin, Richard
    Recent results on the numerical analysis of Algebraic Flux Correction (AFC) finite element schemes for scalar convection-diffusion equations are reviewed and presented in a unified way. A general form of the method is presented using a link between AFC schemes and nonlinear edge-based diffusion scheme. Then, specific versions of the method, this is, different definitions for the flux limiters, are reviewed and their main results stated. Numerical studies compare the different versions of the scheme.