A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.