Abstract
We consider a space-time discretization method for second-order parabolic problems with inhomogeneous (time-dependent) Dirichlet boundary conditions. A combination of a temporal discontinuous Galerkin scheme and a spatial continuous Galerkin scheme is used. In previous work it has been established that the standard semi-discrete temporal scheme has to be modified to obtain an optimal error bound. Here we extend this modification to a fully discrete scheme. For this modified discretization an optimal error bound for the energy norm is derived. Results of experiments confirm the theoretically predicted optimal convergence rates. We are able to pinpoint why the standard CG-DG space-time method (without any modifications) has suboptimal convergence behavior. The method presented here avoids this suboptimality in a way which is computationally very cheap.
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Voulis, I. (2019). An Optimal Order CG-DG Space-Time Discretization Method for Parabolic Problems. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_18
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DOI: https://doi.org/10.1007/978-3-030-14244-5_18
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