Accuracy and convergence of a finite-element algorithm for computational fluid dynamics

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Accuracy and convergence rates with discretization refinement were quantized, in several error norms, by a systematic study of numerical solutions to several non-linear parabolic and a hyperbolic partial differential equation, using linear, quadratic and cubic basis functions. Richardson extrapolation was employed to generate higher-order accurate solutions to facilitate isolation of truncation error in all norms. Direct extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is proven valid for equations characteristic of laminar and turbulent fluid flows.