A staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes : A priori and a posteriori analysis

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)216-228
Journal / PublicationComputers and Mathematics with Applications
Online published10 May 2022
Publication statusPublished - 1 Jul 2022


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.

Research Area(s)

  • Finite volume method, Biharmonic problem, Staggered DG method, Polygonal meshes, Superconvergence, A posteriori error estimator

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