Abstract A new construction method of operator custom-design wavelet finite elements is proposed for analyzing elastic plate problems. The superiority of the method is the construction of decoupling operator custom-design wavelet bases according to the requirements of engineering problems, which leads to highly sparse multiscale system stiffness matrix along diagonal line. The independence and fast computation on each level using the proposed algorithm are realized and the computational efficiency of system of equations is much improved. A multiresolution Lagrange finite element space and multiscale computation theory are constructed. The building method and decoupling condition of operator custom-design wavelet finite element are presented for the elastic plate problems based on stable completion. An adaptive operator custom-design wavelet finite element algorithm is proposed according to two-level relative error estimation. Numerical examples show that the operator custom-design wavelet finite element method is accurate and efficient for solving elastic plate problems.
2013, Vol. 34 
