ISSN:
0271-2091
Keywords:
Least squares
;
Finite elements
;
Non-linear
;
Hyperbolic
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
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.
Additional Material:
6 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650080805
