Parallel, adaptive finite element methods for conservation laws
- RIACS, Moffett Field, CA (United States) Rensselaer Polytechnic Institute, Troy, NY (United States)
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 solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
- Research Organization:
- National Aeronautics and Space Administration, Moffett Field, CA (United States). Ames Research Center
- OSTI ID:
- 6921230
- Journal Information:
- Applied Numerical Mathematics; (Netherlands), Vol. 14; ISSN 0168-9274
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
CONSERVATION LAWS
NUMERICAL SOLUTION
PARALLEL PROCESSING
ALGORITHMS
PARTIAL DIFFERENTIAL EQUATIONS
FINITE ELEMENT METHOD
HYPERCUBE COMPUTERS
RUNGE-KUTTA METHOD
CALCULATION METHODS
COMPUTERS
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
PROGRAMMING
990200* - Mathematics & Computers