Istituto di Scienza e Tecnologie dell'Informazione     
Cella A., Monacci L. A numerical appraisal of the Galerkin-finite element method for linear and nonlinear parabolic operators. Internal note IEI-B75-08, 1975.
The Galerkin finite element method is now a well established procedure for the numerical solution of both linear and nonlinear parabolic problems. For the analyst and for the program user, however, several questions remain open as far as the choice of the numerical integration scheme, and for the allocation of the discretization parameters. Focasing at first on the conduction-diffusion equations, a parametric numerical error analysis has been performed on one and two dimensional test problems for which the exact solution is known. From the analysis of the error curves several conclusions have been drawn as fas as the "optimal" values of the parameters. A nonlinear heat conduction problem has been subsequently analyzed, where the nonlinearity is concentrated in the conductivity coefficient. Here the pattern of convergence to steady-state has been analyzed. The reliability of predictor-corrector schemes as against extrapolation schemes has been confirmed.

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