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 H2 piecewise polynomial approximants with hp -optimal approximation properties over the given meshes. The hp -optimality is also discussed for C -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 presence of singular essential boundary conditions.

Dong, Z., Mascotto, L. (2023). hp-Optimal Interior Penalty Discontinuous Galerkin Methods for the Biharmonic Problem. JOURNAL OF SCIENTIFIC COMPUTING, 96(1) [10.1007/s10915-023-02253-y].

hp-Optimal Interior Penalty Discontinuous Galerkin Methods for the Biharmonic Problem

Mascotto, L
2023

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 H2 piecewise polynomial approximants with hp -optimal approximation properties over the given meshes. The hp -optimality is also discussed for C -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 presence of singular essential boundary conditions.
Articolo in rivista - Articolo scientifico
A priori error estimation; Discontinuous Galerkin; Optimal convergence; p-version;
English
6-giu-2023
2023
96
1
30
partially_open
Dong, Z., Mascotto, L. (2023). hp-Optimal Interior Penalty Discontinuous Galerkin Methods for the Biharmonic Problem. JOURNAL OF SCIENTIFIC COMPUTING, 96(1) [10.1007/s10915-023-02253-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/419938
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