Parallel, adaptive finite element methods for conservation laws

Journal Article · Sat Jan 01 04:00:00 EST 1994 · Applied Numerical Mathematics; (Netherlands)

DOI:https://doi.org/10.1016/0168-9274(94)90029-9· OSTI ID:6921230

Biswas, R; Devine, K D; Flaherty, J E ^[1]

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1. 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), Journal Name: Applied Numerical Mathematics; (Netherlands) Vol. 14; ISSN 0168-9274; ISSN ANMAEL
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
CALCULATION METHODS
COMPUTERS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
HYPERCUBE COMPUTERS
ITERATIVE METHODS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING
RUNGE-KUTTA METHOD