finite element method node point based strong form • strong form / residual format • residuals strong form finite element method
finite element method node point based boundary conditions • dirichlet / essential boundary conditions • neumann / natural boundary conditions boundary conditions finite element method
finite element method node point based weak form • weak form • weak form expressions weak form finite element method
finite element method node point based weak form • integration by parts • gauss theorem & boundary conditions • weak form weak form finite element method
temporal discretization node point based • discretization • time discrete weak form • interpolation of material time derivatives euler backward temporal discretization finite element method
spatial discretization node point based • discretization • interpolation of test functions • interpolation of trial functions spatial discretization finite element method
finite element method node point based discrete residuals • discrete residual format • discrete residuals discrete residuals finite element method
finite element method node point based linearization • linearization / newton raphson scheme • incremental residual • system of equations linearization finite element method
finite element method node point based linearization • iteration matrices linearization finite element method
simultaneous solution node point based loop over all time steps global newton iteration loop over all elements loop over all quadrature points evaulate balance of mass and momentum determine element residuals & partial derivatives determine global residuals and iterational matrices determine and determine state of biological equilibrium simultaneous solution finite element method
finite element method integration vs node point based integration point - discontinuous solution finite element method
integration vs node point based node point - continuous solution finite element method
integration vs node point based node point - continuous solution finite element method