An operator custom-design wavelet-based thin plate element and its application

An adaptive operator custom-design wavelet finite element method based on the lifting scheme is proposed and a new operator custom-design wavelet thin plate element is constructed. A two-dimensional Hermite-type multiresolution finite element space and two-level relation are built. The inner production equation of scaling functions and wavelet functions of thin plate structure, also called the operator, is derived based on the general variational principle. The construction method of operator custom-design wavelet finite elements based on the lifting scheme is presented to meet the operator-orthogonalization. The property of the method is that the wavelets can be designed with the specified feature depending on the requirements of the problems. An adaptive operator custom-design wavelet finite element method is presented on the two-level error estimation, which can solve the thin plate problems efficiently by adding operator custom-design wavelets into the local domains higher than the threshold value. The operator custom-design wavelet finite element method saves a great deal of preprocessing time of refining the meshes or increasing the approximating order of the interpolating functions and realizes efficient decoupling computation of thin plate problems.