A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

By Igor Mozolevski, Endre Süli. 2003

105 citations recorded by the source corpus.

Abstract We consider the hp-version of the discontinuous Galerkin finite element approximation of boundary value problems for the biharmonic equation. Our main concern is the a priori error analysis of the method, based on a nonsymmetric bilinear form with interior discontinuity penalization terms. We establish an a priori error bound for the method which is of optimal order with respect to the mesh size h , and nearly optimal with respect to the degree p of the polynomial approximation. For analytic solutions, the method exhibits an exponential rate of convergence under p- refinement. These results are shown in the DG-norm for a general shape regular family of partitions consisting of d-dimensional parallelepipeds. The theoretical results are confirmed by numerical experiments. The method has also been tested on several practical problems of thin-plate-bending theory and has been shown to be competitive in accuracy with existing algorithms.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7a5d563e22d9583a7a1250404e5dc10c647055e1

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Discontinuous Galerkin methods for the biharmonic problem (2009, unknown): “6 describes the hp-convergence of the interior penalty DG method when pκ ≥ 3, κ ∈ T , and coincides with the corresponding error bound first derived in [16, 22], albeit with different method of proof.”
An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems (2011, methodology): “Recently hp-version interior penalty DG finite element methods for the biharmonic problem have been derived in [22, 25, 23, 17], where the stability and a priori error bounds are presented in various settings.”