Journal of the Chinese Society of Mechanical Engineers
Abstract: A p-version based least-squares finite-element method (LSFEM) is presented for general second-order partial differential equations. The resulting system of equations of the formulation is symmetric and positive-definite. Various preconditioned iterative solvers, such as, conjugate gradient (CG), generalized minimum residual (GMRES), quasi-minimum residual (QMR) methods and their variants were used to solve the algebraic system of equations and their performance were compared. The method was applied to both linear and non-linear partial differential equations which encounter the sharp gradient solution.