Discontinuous Galerkin method based on non-polynomial approximation spaces
- 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, Vol. 218, Issue 1; Other Information: DOI: 10.1016/j.jcp.2006.02.013; PII: S0021-9991(06)00085-4; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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