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arXiv · 1501.04765

Discontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions

Paola F. Antonietti·Maurizio Grasselli·Simone Stangalino·Marco Verani
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Abstract

In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete scheme. More precisely, using polynomials of degree $p\geq 1$ on meshes with granularity $h$ along with a backward Euler time-stepping scheme with time-step $\Delta t$, we prove that the fully-discrete solution is bounded by the data and it converges, in a suitable (mesh-dependent) energy norm, to the exact solution with optimal order $h^p + \Delta t$. The sharpness of the theoretical estimates are verified through several numerical experiments.

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Paola F. Antonietti, Maurizio Grasselli, Simone Stangalino, Marco Verani. 2015-01-20. Discontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions. https://arxiv.org/abs/1501.04765

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