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math.NA2018
The optimal convergence rate of monotone schemes for conservation laws in the Wasserstein distance
Adrian Montgomery Ruf, Espen Sande, Susanne Solem
In 1994, Nessyahu, Tadmor and Tassa studied convergence rates of monotone finite volume approximations of conservation laws. For compactly supported, $\Lip^+$-bounded initial data…
math.AP2018
A convergent finite difference scheme for the Ostrovsky--Hunter equation with Dirichlet boundary conditions
Johanna Ridder, Adrian Montgomery Ruf
We prove convergence of a finite difference scheme to the unique entropy solution of a general form of the Ostrovsky--Hunter equation on a bounded domain with non-homogeneous Diric…
math.AP2018
Convergence of a Full Discretization for a Second-Order Nonlinear Elastodynamic Equation in Isotropic and Anisotropic Orlicz Spaces
Adrian Montgomery Ruf
In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exh…