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Journal Articles Journal of Scientific Computing Year : 2023

hp-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem

Abstract

We prove hp-optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) for the biharmonic problem with homogeneous essential boundary conditions. We consider tensor product-type meshes in two and three dimensions and triangular meshes in two dimensions. An essential ingredient in the analysis is the construction of a global H 2 piecewise polynomial approximants with hp-optimal approximation properties over the given meshes. The hp-optimality is also discussed for C 0-IPDG in two and three dimensions and the stream formulation of the Stokes problem in two dimensions. Numerical experiments validate the theoretical predictions and reveal that p-suboptimality occurs in the presence of singular essential boundary conditions.
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Dates and versions

hal-03889072 , version 1 (07-12-2022)
hal-03889072 , version 2 (03-05-2023)

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Zhaonan Dong, Lorenzo Mascotto. hp-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem. Journal of Scientific Computing, In press, 96 (30), pp.30. ⟨10.1007/s10915-023-02253-y⟩. ⟨hal-03889072v2⟩
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