Orthogonal finite functions on triangular grids and a hybrid variational-grid method related to their applications

Orthogonal finite functions for triangular grids are proposed. It is shown that these functions form a basis in a space of continuous functions, and the accuracy of the approximations is estimated. A variational-grid method is developed which is based on the mixed Reissner variational principle. The satisfactory accuracy of the resulting approximations is demonstrated by comparing the results obtained by the proposed method with those obtained by other variational-grid methods, finite element method, and classical series methods. (CSA)