RESEARCH ADVANCES IN THE TREFFTZ FINITE ELEMENT METHOD

The Trefftz finite element method (TFEM) is an efficient numerical approach with many joint advantages of the conventinal finite and boundary element methods. Based on the mutual independent interpolation modes, the finite element formulation involving the boundary integrations only is derived by incorporating the hybrid functional and the Gaussian divergence theorem. The research advances in the internal interpolation function, the treatment of the source term, the special-purpose element and the nonisotropic material during the past decade (2007-2016) are reviewed and several directions are pointed out for the future development.