Krivodonova, LiliaSmirnov, Alexey2022-06-152022-06-152021-10-05https://doi.org/10.48550/arXiv.2110.00067http://hdl.handle.net/10012/18378The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging to extend this approach to two-dimensional problems. Using the anisotropic definition for discrete total variation (TV), it was shown in [14] that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definitionenhyperbolic conservation lawstotal variation diminishing schemesdiscontinuous Galerkin methodhigh-order methodsPreprint