Discontinuous Galerkin methods for the biharmonic problem

By Emmanuil H. Georgoulis, Paul Houston. 2009

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This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold et al. (2001/2002, SIAM J. Numer. Anal., 39, 1749-1779) developed for the Poisson problem, to the design of DG methods via an appropriate choice of numerical flux functions for fourth-order problems; as an example, we retrieve the interior penalty DG method developed by Suli & Mozolevski (2007, Comput. Methods Appl. Mech. Eng.,196, 1851-1863). The second part of this work is concerned with a new a priori error analysis of the hp-version interior penalty DG method, when the error is measured in terms of both the energy norm and the L 2 -norm, as well as certain linear functionals of the solution, for elemental polynomial degrees p ≥ 2. Also, provided that the solution is piecewise analytic in an open neighbourhood of each element, exponential convergence is also proved for the p-version of the DG method. The sharpness of the theoretical developments is illustrated by numerical experiments.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4b701dcd4e859647427b1ba2e4c8184ca07d65bf

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems (2011, methodology): “this is a variant of the model problem considered in [25], cf. also [ 17 ].”