hp-VERSION DISCONTINUOUS GALERKIN METHODS FOR HYPERBOLIC CONSERVATION LAWS: A PARALLEL ADAPTIVE STRATEGY
نویسنده
چکیده
This paper describes a parallel algorithm based on discontinuous hp-finite element approximations of linear, scalar, hyperbolic conservation laws. The paper focuseson the development of an elTcctiveparallel adaptive strategy for such problems. Numerical experimeOlssuggest that these techniques are highly parallelizable and exponentially convergent, thereby yielding cflicien.:yIllany times superior to conventional schemes for hyperbolic problems.
منابع مشابه
A Parallel hp-Adaptive Discontinuous Galerkin . Method for Hyperbolic Conservation Laws
This paper describes a parallel adaptive strategy based on discontinuous hp-finite element approximations oflinear, scalar, hyperbolic conservation laws. The paper focuses on the development of an effective parallel adaptive strategy for such problems, Numerical experiments suggest that these techniques arc highly parallelizablc a.nd deliver super-linear rates of convergence, thereby yielding e...
متن کاملhp-Version discontinuous Galerkin methods for hyperbolic conservation laws
Thc devclopment of hp·version discontinuous Galerkin methods for hyperholic conservalion laws is presented in this work. A priori error estimates are dcrived for a model class of linear hyperbolic conservation laws. These estimates arc obtained using a ncw mesh-dependcnt norm that rel1ects thc dependcnce of the approximate solution on thc local element size and the local order of approximation....
متن کاملSpectral/hp Element Method with Hierarchical Reconstruction for Solving Nonlinear Hyperbolic Conservation Laws
The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservati...
متن کاملParallel , Adaptive Finite Element Methods for Conservation Laws
Abstract: We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solutio...
متن کاملShock Detection and Limiting with Discontinuous Galerkin Methods for Hyperbolic Conservation Laws
We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinuities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting discontinuities in such variables as density ...
متن کامل