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تسجيل مستخدم جديدDiscontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions
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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 $pgeq 1$ 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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