Convenient system of FEM test functions for computational fluid dynamics

For the development of finite element schemes, a fundamentally new system of test functions defined on a finite element that is a convex quadrilateral is proposed. Due to the remarkable properties of the system (specifically, mutual orthogonality), the resulting matrices can be simplified and the corresponding construction procedures can be made more transparent, especially for problems in computational fluid dynamics. Thus, the system of test functions may play an important role in finite element methods as applied to two-dimensional problems.