caa a22 4500 475777077 CHVBK 20180406123634.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1007633810484 doi (NATIONALLICENCE)springer-10.1023/A:1007633810484 High Order Numerical Discretization for Hamilton-Jacobi Equations on Triangular Meshes [Elektronische Daten] [Steeve Augoula, Rémi Abgrall] In this paper we construct several numerical approximations for first order Hamilton-Jacobi equations on triangular meshes. We show that, thanks to a filtering procedure, the high order versions are non-oscillatory in the sense of satisfying the maximum principle. The methods are based on the first order Lax-Friedrichs scheme [2] which is improved here adjusting the dissipation term. The resulting first order scheme is ε-monotonic (we explain the expression in the paper) and converges to the viscosity solution as $$\mathcal{O}(\sqrt {\Delta t} )$$ for the L ∞-norm. The first high order method is directly inspired by the ENO philosophy in the sense where we use the monotonic Lax-Friedrichs Hamiltonian to reconstruct our numerical solutions. The second high order method combines a spatial high order discretization with the classical high order Runge-Kutta algorithm for the time discretization. Numerical experiments are performed for general Hamiltonians and L 1, L 2 and L ∞-errors with convergence rates calculated in one and two space dimensions show the k-th order rate when piecewise polynomial of degree k functions are used, measured in L 1-norm. Plenum Publishing Corporation, 2000 Hamilton-Jacobi equation nationallicence viscosity solution nationallicence numerical Hamiltonian nationallicence $$\mathbb{P}^k $$ triangulation nationallicence ε -monotonicity nationallicence Augoula Steeve E-mail: augoula@math.u-bordeaux.fr aut Abgrall Rémi E-mail: abgrall@math.u-bordeaux.fr aut Journal of Scientific Computing Kluwer Academic Publishers-Plenum Publishers 15/2(2000-06-01), 197-229 0885-7474 15:2<197 2000 15 10915 https://doi.org/10.1023/A:1007633810484 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1007633810484 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Augoula Steeve E-mail: augoula@math.u-bordeaux.fr aut NATIONALLICENCE 700 1- Abgrall Rémi E-mail: abgrall@math.u-bordeaux.fr aut NATIONALLICENCE 773 0- Journal of Scientific Computing Kluwer Academic Publishers-Plenum Publishers 15/2(2000-06-01), 197-229 0885-7474 15:2<197 2000 15 10915 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer