Fundamental Concepts of Finite Element Method (FEM)

摘要: In this chapter the basic principles of FEM are systematically developed and reviewed for prototypical advection-dispersion equations (ADE’s). The different spatial temporal discretization techniques addressed. important approximate solutions divergence convective forms ADE carefully developed. Emphasis is given on adaptive solution strategies. Implicit explicit time integration methods compared. It clearly shows superiority implicit strategies present problem classes, in particular automatic error-controlled predictor-corrector schemes favorited. Upwind thoroughly discussed examined comparison to standard Galerkin-based (GFEM). Stability error analyses favorite presented some detail. Techniques solving resulting matrix discussed. Of interest nonlinear by using Picard Newton iteration techniques, which embedded stepping transient problems. A focus derived quantities, i.e., evaluation fluxes balance quantities. shown that locally conservative.