In this paper, a staggered cell-centered discontinuous Galerkin method is developed for the biharmonic problem with the Steklov boundary condition. Our approach utilizes a first-order system form of the biharmonic problem and can handle fairly general meshes possibly including hanging nodes, which favors adaptive mesh refinement. Optimal order error estimates in L2 norm can be proved for all the variables. Moreover, the approximation of the primal variable superconverges in L2 norm to a suitably chosen projection without requiring additional regularity. Residual type error estimators are proposed, which can guide adaptive mesh refinement to deliver optimal convergence rates even for solutions with singularity. Numerical experiments confirm that the optimal convergence rates in L2 norm can be achieved for all the variables. Moreover, all the provided residual type error estimators show the desired results. In particular, the numerical results demonstrate that the proposed scheme on a polygonal approximation of the disk works well for the classic Babuška example.
|Number of pages||13|
|Journal||Computers and Mathematics with Applications|
|Publication status||Published - 2022 Jul 1|
Bibliographical noteFunding Information:
This author was supported by a grant from City University of Hong Kong (Project No. 7200699).This author was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (NRF-2019R1A2C2090021 and NRF-2022R1A2B5B02002481).
© 2022 Elsevier Ltd
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics