Abstract
A least-squares finite element method has been developed for the solution of nonlinear hyperbolic problems. The formulation of the problem is achieved via a backward differencing in time leading to the semi-discretized form of the governing differential equations. Temporal discretization of the governing equation produces a residual which is then minimized in a least-square sense resulting in the variational form of the problem. The discretization of the variational statement by finite elements leads to a set of algebraic equations to be solved for nodal unknowns. The possibilities of using linear and quadratic elements is investigated and examined numerically. Application of the method to solve Burgers equation , nozzle and dam-break problems are also presented.
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