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The least-squares finite element method (LSFEM) has many attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike Galerkin finite element method (GFEM). However, the higher continuity requirements for second-order terms in the governing equations force the introduction of additional unknowns through the use of an equivalent first-order system of equations or the use of C¹ continuous basis functions, limiting the application of LSFEM to large-scale practical problems. A novel finite element method is proposed that employs a least-squares method for first-order derivatives and a Galerkin method for second order derivatives, thereby avoiding the need for additional unknowns required by a pure LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the least-squares method. The method is stable for convection-dominated flows and allows for equal-order basis functions for both pressure and velocity. Various incompressible and compressible flow benchmark problems have been solved using low-order C continuous elements.
About the author
Born on Feb 26,1988 in India. He received B.TECH (Electronics and instrumentation)from I.E.T M.J.P Rohilkhand Univ. Bareilly,India in 2011.He also did M.E in Instrumentation and Control from Thapar Univ. Patiala,India in 2013. His areas of interest include optimal control, Soft Computing and process control.
