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The Lax-Friedrichs method in one-dimensional hemodynamics
Anika Beckers, Niklas Kolbe
The discretization of reduced one-dimensional hyperbolic models of blood flow using the Lax-Friedrichs method is discussed. Employing the well-established central scheme in this do…
Influx ratio preserving coupling conditions for the networked Lighthill-Whitham-Richards model
Niklas Kolbe
A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the t…
Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation
Kharisma Surya Putri, Tatsuki Mizuochi, Niklas Kolbe +1
A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is pr…
A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model
Jan Giesselmann, Niklas Kolbe
We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent and periodic boundary conditions. We deri…