A decoupled finite element method for the triharmonic equation

A decoupled finite element method for the triharmonic equation in two dimensions is developed in this paper. The triharmonic equation can be decoupled into two biharmonic equations and one symmetric tensor-valued Stokes equation. Two biharmonic equations are discretized by the Morley element. An H1(S)-conforming finite element in arbitrary dimension is constructed and applied for solving the tensor-valued Stokes equation. The convergence analysis is presented for the resulting discrete method. Numerical results are provided to verify the theoretical convergence rates.(c) 2023 Elsevier Ltd. All rights reserved.