Solving the nonlinear Poisson-type problems with F-Trefftz hybrid finite element model

A hybrid finite element model based on F-Trefftz kernels (fundamental solutions) is formulated for analyzing Dirichlet problems associated with two-dimensional nonlinear Poisson-type equations including nonlinear Poisson–Boltzmann equation and diffusion–reaction equation. The nonlinear force term in the Poisson-type equation is frozen by introducing the imaginary terms at each Picard iteration step, and then the induced Poisson problem is solved by the present hybrid finite element model involving element boundary integrals only, coupling with the particular solution method with radial basis function interpolation. The numerical accuracy of the present method is investigated by numerical experiments for problems with complex geometry and various nonlinear force functions.

► Application of F-Trefftz function to hybrid finite element method. ► Developing efficient nonlinear iterative algorithm for handling nonlinear terms. ► Element boundary integrals used in hybrid finite element approach. ► Application of radial basis function to hybrid finite element formulation.