Parallel Partitioning Strategies for the Adaptive Solution of Conservation Laws, Rensselaer Polytechnic

order accurate discontinuous discontinuous nite element solution of the 2D Euler equations, A massively parallel adaptive nite element method with dynamic load balancing, SAND 93-0936C (1993). 21. K. Eriksson and C. Johnson, Adaptive nite element methods for parabolic problems I: A linear model problem, SIAM J. Adaptive nite element methods for parabolic problems IV: A nonlinear model problem, SIAM J. a nite element method for solving the neutron transport equation, Mathematical aspects of nite elements in partial diierential equations (C. de Boor, A space-time discontinuous Galerkin method for the time accurate numerical solution of hyperbolic conservation laws, Parallel adaptive mesh reene-ment and redistribution on distributed memory computers, Comput. 32 amount of degrees of freedom per element, and hence more computations per element are necessary, its extremely local domain of dependency allows a very eecient parallelization that by far compensates for the extra amount of local computations. Acknowledgments. The authors want to thank X. Makridakis for bringing to their attention the reference 3], and H. Atkins for helpful discussions in the computation. A characteristics-mixed nite element method for advection-dominated transport problems, SIAM J. A high-order accurate discontinuous nite element method for the numerical solution of the compressible Navier-Stokes equations, J. A high-order accurate discon-tinuous nite element method for inviscid and viscous turbomachinery ows, Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode, J. 31 where P h (u) is either the value of P h (u) at e from the interior of K or from its exterior, and k P h (p)] k L 2 (e) d k ((x) ?1=2 k P h (p) k L 2 (KK e) ; where P h (p)] denotes the jump at e of P h (p). Finally, we also use the following result: k p ? P h (p) k L 2 (0;1) d g k (x) k+1 j p j H (k+1) (0;1) d ; All these approximation results can be found in Ciarlet 11], for example. 4. Concluding remarks. In this paper, we have considered the so-called LDG methods for convection-diiusion problems. For scalar problems in multidimensions, we have shown that they are L 2-stable and that in the linear case, they are of order k if polynomials of order k are used. We have also shown that this estimate is sharp and have displayed the strong dependence of the order of convergence of the LDG methods on the choice of …