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CONTINUUM BOUNDARY VALUE PROBLEMS AND
USE OF CONTINUOUS
PIECEWISE DEFINED TRIAL FUNCTIONS AND THE FINITE
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analysis applied approximate solution boundary conditions Chapter coefficients condition of Eq consider coordinates defined derivatives determine differential equation discretization discretization error displacement dNf dNf dNf domain dx dx dy dy dy eigenvalues elastic element matrices element shape functions equation set equation system Euler equation evaluated exact solution expansion expression FIGURE finite difference method finite element method form of Eq formulation functions Nm Galerkin method governing equation heat conduction hierarchical higher order illustrated integration linear elements mapping matrix mesh point natural boundary condition nodes numbered nonlinear nonzero obtained one-dimensional ordinary differential equations parameters piecewise linear point collocation point spacing problem of Example procedures produced quadratic elements reader rectangular elements region shown in Fig simple solved temperature tion trial function set triangular elements two-dimensional typical variational principle vector weighted residual method weighted residual statement weighting functions write zero