| Interpolations which are smooth and bounded can be constructed over any two dimensional polygonal domain, including those with concavities and inclusions. Like boundary element test functions, they depend only on the boundary values. Unlike the boundary element method formulations, they satisfy linear essential boundary conditions exactly and do not depend on a Greens' function solution to the governing field equation. In other words, they are Ritz type coordinate functions which apply to any polygonal domain. The interpolations satisfy element level constancy and linear patch tests and perform well in approximation of potential field solutions. Similar functions, applicable only to convex polygons, have been applied successfully to biomedical problems including skull growth and heart function analyses. No smooth kinematic concave polygonal element description of any type is presented in the available finite element, boundary element or computational geometry literature. |
