Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem

摘要: We describe in this report various methods, iterative and "almost direct," for solving the first biharmonic problem on general two-dimensional domains once continuous has been approximated by an appropriate mixed finite element method. Using approach described we recover some well known methods equation as a system of coupled harmonic equations, but discussed here are completely new, including conjugate gradient type algorithm. In last part discuss extension above to numerical solution two dimensional Stokes p- connected (p $\geq$ 1) through stream function-vorticity formulation.