| Issue |
ESAIM: M2AN
Volume 60, Number 1, January-February 2026
|
|
|---|---|---|
| Page(s) | 247 - 272 | |
| DOI | https://doi.org/10.1051/m2an/2025097 | |
| Published online | 23 February 2026 | |
Numerical solution of two dimensional scalar conservation laws using compact implicit numerical schemes on Cartesian meshes
Department of Mathematics and Descriptive Geometry, Slovak University of Technology in Bratislava, Bratislava, Slovakia
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
28
August
2024
Accepted:
2
December
2025
Abstract
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order accurate parametric scheme based on the finite volume method including simple variants of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) approximations. To avoid oscillatory numerical solutions for large time steps, we propose limiting in time which is provable non-oscillatory in the case of linear advection equation with variable velocity. We present numerical experiments for representative linear and nonlinear problems.
Mathematics Subject Classification: 35L60 / 35L65 / 65M08 / 65M12
Key words: Compact implicit discretization / high-resolution numerical method / positive coefficients scheme / advection equation / Burgers equation
© The authors. Published by EDP Sciences, SMAI 2026
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