A stable least-squares finite element method for non-linear hyperbolic problems |
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Authors: | B. N. Jiang Graham F. Carey |
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Abstract: | A class of stable least-square finite element methods for non-linear hyperbolic problems is developed and some exploratory studies made. The methods are based on modifying the L2-norm of the. residual and a related approximation to the H1-norm of the residual. The effect of the additional terms in these residual functionals is to introduce a dissipative effect proportional to the solution gradient. This acts to stabilize the solution for non-linear hyperbolic problems which generate shocks. Numerical results for a one-dimensional nozzle and shock tube problem demonstrate the accuracy and stability of the method. Results are for an implicit scheme and calculations for linear, quadratic and cubic elements are given. |
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Keywords: | Least squares Finite elements Non-linear Hyperbolic |
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