Discontinuous Galerkin method based on non-polynomial approximation spaces

Journal Article · Tue Oct 10 04:00:00 EDT 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2006.02.013· OSTI ID:20840356

Ling, Yuan ^[1]; Chiwang, Shu ^[1]

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1. Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States)

In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L {sup 2} stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.

• OSTI ID: 20840356
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 218; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
APPROXIMATIONS
BOUNDARY CONDITIONS
ERRORS
GALERKIN-PETROV METHOD
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
STEADY-STATE CONDITIONS
TIME DEPENDENCE