Accuracy and convergence of a finiteelement algorithm for computational fluid dynamics
Abstract
A Galerkinweighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initialboundary value problems. Accuracy and convergence rates with discretization refinement were quantized, in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation, using linear, quadratic and cubic basis functions. Richardson extrapolation was employed to generate higherorder 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 1978
 Bibcode:
 1978PhDT.......131S
 Keywords:

 Algorithms;
 Finite Element Method;
 Fluid Dynamics;
 Boundary Value Problems;
 Extrapolation;
 Fluid Flow;
 Partial Differential Equations;
 Problem Solving;
 Fluid Mechanics and Heat Transfer