arXiv subjects

Anika Beckers

Publications and source records attributed to Anika Beckers.

3 recordsLinked to original sources

arXiv2026

A Third-Order Maximum-Principle-Preserving CWENO Scheme for Two-Dimensional Nonlocal Conservation Laws

We present a third-order finite volume central WENO scheme for systems of nonlocal conservation laws in two spatial dimensions. The CWENO reconstruction of the conservative variable provides polynomials that can be evaluated in the entire domain, which is of advantage when approximating the nonlocal terms. Moreover, this method can be augmented with a limiter that preserves the maximum-principle and especially positivity of the solution.

math.NA↗

arXiv2026

Monotone-based Numerical Schemes for Two-Dimensional Systems of Nonlocal Conservation Laws

We present a general class of numerical schemes for two-dimensional systems of nonlocal conservation laws, which are based on utilizing well-known monotone numerical flux functions after suitably approximating the nonlocal terms. The considered systems are weakly coupled by the nonlocal terms and the underlying flux function is rather general to guarantee that our results are applicable to a wide range of common nonlocal models. We state sufficient conditions to ensure the convergence of the monotone-based numerical schemes to the unique weak entropy solution. Moreover, we provide an error estimate that yields the convergence rate of $\mathcal{O}(\sqrt{\Delta t})$ for the numerical approximations of the solution. Our results include an existence and uniqueness proof of the nonlocal system, too. Numerical results illustrate our theoretical findings.

math.NA↗

arXiv2025

The Lax-Friedrichs method in one-dimensional hemodynamics

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 domain significantly simplifies the implementation of specific boundary and coupling conditions in vascular networks accounting e.g. for a periodic heart beat, vascular occlusions, stented vessel segments and bifurcations. In particular, the coupling of system extensions modeling patient specific geometries and therapies can be realized without information on the eigenstructure of the models. For the derivation of the scheme and the coupling conditions a relaxation of the model is considered and its discrete relaxation limit evaluated. Moreover, a second order MUSCL-type extensions of the scheme is introduced. Numerical experiments in uncoupled and coupled cases that verify the consistency and convergence of the approach are presented.

math.NA↗