## A p-version finite element method for steady incompressible fluid flow and convective heat transfer |

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arbitrary parameters Asymmetric Sudden Expansion Babuska-Brezzi condition continuity equation convection-conduction equation convective heat transfer converged d2v d2v degrees of freedom delta dimensionless dP 1 d2u driven cavity dv dv dP dx dy dx dx J dx dy J dy eqn A.2 equal order interpolation equation in section exact solution Figure 17 finite element method finite element solutions flow and convective fluid dynamics functions and nodal h-p version highly accurate solutions incompressible fluid flow L2 norm least-squares formulation Navier-Stokes equations nodal variables node non-symmetric matrix Numerical Example numerical results one-dimensional Burgers p-level p-refinement p-version approximation functions p-version elements p-version finite element Peclet numbers Petrov-Galerkin formulation Petrov-Galerkin weighting presented in figure pressure contours Reynolds number shear stress shown in figure Smith-Hutton problem solution error solutions obtained Solutions to Burgers spectral methods standard Galerkin formulation steady-state limit streamline plot sudden expansion problem Taylor series upwinding parameter velocity and pressure weighted residual formulation