Design of an optimal grid for finite element methods in incompressible fluid flow problems

Finite element solutions of improved quality are obtained by optimizing the location of nodes of the finite element grid, while keeping the number of degrees of freedom fixed. The formulation of the grid optimization problem is based on the reduction of error associated with interpolation of the exact solution, using functions from the finite element space. Element sizes are selected as design variables: length in R and area in R. Approximate optimal conditions are introduced to obtain a set of operationally useful equations that can be used as guidelines for construction of improved grids. Example problems are given for illustrations.