30 research outputs found
Patankar-Type Runge-Kutta Schemes for Linear PDEs
No full textWe study the local discretization error of Patankar-type Runge-Kutta methods
applied to semi-discrete PDEs. For a known two-stage Patankar-type scheme the
local error in PDE sense for linear advection or diffusion is shown to be of
the maximal order for sufficiently smooth and positive
exact solutions. However, in a test case mimicking a wetting-drying situation
as in the context of shallow-water flows, this scheme yields large errors in
the drying region. A more realistic approximation is obtained by a modification
of the Patankar approach incorporating an explicit testing stage into the
implicit trapezoidal rule
Preface of “The Second Symposium on Border Zones Between Experimental and Numerical Application Including Solution Approaches By Extensions of Standard Numerical Methods”
No full text
On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection‑Diffusion Equations
No full textGefördert im Rahmen des Projekts DEA
Ein diskontinuierliches Galerkin-Verfahren hoher Ordnung auf Dreiecksgittern mit modaler Filterung zur Lösung hyperbolischer Erhaltungsgleichungen
No full textZugleich: Dissertation, Universität Kassel, 201
A comparative Fourier analysis of discontinuous Galerkin schemes for advection–diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization
No full textGefördert im Rahmen des Projekts DEA
Numerical Methods for Fluid Flow: High Order SBP Schemes, IMEX Advection-Diffusion Splitting and Positivity Preservation for Production-Destruction PDEs
No full text
Fourier Analysis of DG Schemes for Advection‐Diffusion
No full textGefördert im Rahmen des Projekts DEA
Positivity Preserving Implicit and Partially Implicit Time Integration Methods in the Context of the DG Scheme Applied to Shallow Water Flows
No full text
