An efficient L2 Galerkin finite element method for multi-dimensional non-linear hyperbolic systems

An L2 Galerkin approximation is obtained by the use of specially chosen spaces of trial and test functions. The method combines the features of the orthogonal collocation and Galerkin finite element methods. This new algorithm can be more efficient by orders of magnitude than conventional discontinuous Galerkin finite element procedures in solving non-linear problems which require frequent reformulation of the coefficient matrices and right-hand-side vectors.

[1]  P. Raviart,et al.  On a Finite Element Method for Solving the Neutron Transport Equation , 1974 .

[2]  A finite element method for first order hyperbolic equations , 1975 .

[3]  J. Z. Zhu,et al.  The finite element method , 1977 .

[4]  G. Sod.  A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[5]  G. Pinder,et al.  A collocation finite element method for potential problems in irregular domains , 1979 .

[6]  M. Fortin,et al.  Mixed finite-element methods for incompressible flow problems☆ , 1979 .

[7]  W. D. Liam Finn,et al.  Space‐time finite elements incorporating characteristics for the burgers' equation , 1980 .

[8]  O. C. Zienkiewicz,et al.  An adaptive finite element procedure for compressible high speed flows , 1985 .

[9]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems , 1986 .

[10]  Juhani Pitkäranta,et al.  An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation , 1986 .

[11]  J. T. Oden,et al.  Adaptive finite element methods for high‐speed compressible flows , 1987 .

[12]  Moshe Shpitalni,et al.  Finite element mesh generation via switching function representation , 1989 .

[13]  P. Bar-Yoseph,et al.  Space-time discontinuous finite element approximations for multi-dimensional nonlinear hyperbolic systems , 1989 .