Journal of Scientific Computing

, Volume 66, Issue 3, pp 1260–1280 | Cite as

Discontinuous Galerkin Approximation of Linear Parabolic Problems with Dynamic Boundary Conditions

  • P. F. Antonietti
  • M. Grasselli
  • S. Stangalino
  • M. Verani
Article

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 \(p\ge 1\) 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.

Keywords

Discontinuous Galerkin Dynamic boundary conditions Parabolic problems Error estimates 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • P. F. Antonietti
    • 1
  • M. Grasselli
    • 2
  • S. Stangalino
    • 1
  • M. Verani
    • 1
  1. 1.MOX-Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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