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Weighted Residual and Variational Methods
The Finite Element Technique
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applied approximate aquifer arbitrary assume boundary conditions coefficients consider constant continuity equation convergence coordinates corresponding cubic Darcy's law define degrees of freedom differential diffusion dx dy element matrices elevation energy equilibrium equations essential boundary essential boundary conditions exact solution Example expression finite difference Finite Element Analysis Finite Element Method flow fluid flux formula free surface Galerkin's method gives governing equations Hence incompressible initial integration interpolation functions inviscid iteration Laplace equation linear mass matrix mesh momentum equations natural boundary conditions nodal unknowns Note obtain orthogonal parameters particle positive definite potential prescribed pressure problem quadratic quadratic function rectangular element Reynolds number scheme shallow water equations shown in Figure solve steady stream function streamlines Substituting symmetric system of equations trapezoidal rule triangular element two-dimensional variational statement vector velocity viscous vorticity weighted residual write written zero