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 (Formula presented.) on meshes with granularity h along with a backward Euler time-stepping scheme with time-step (Formula presented.), 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 (Formula presented.). The sharpness of the theoretical estimates are verified through several numerical experiments.

Discontinuous Galerkin Approximation of Linear Parabolic Problems with Dynamic Boundary Conditions

ANTONIETTI, PAOLA FRANCESCA;GRASSELLI, MAURIZIO;STANGALINO, SIMONE;VERANI, MARCO
2016

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 (Formula presented.) on meshes with granularity h along with a backward Euler time-stepping scheme with time-step (Formula presented.), 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 (Formula presented.). The sharpness of the theoretical estimates are verified through several numerical experiments.
Discontinuous Galerkin; Dynamic boundary conditions; Error estimates; Parabolic problems; Software; Computational Theory and Mathematics; Theoretical Computer Science; Engineering (all)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1004534
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