A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs
| Autor: | Gang Chen, Guosheng Fu, Yangwen Zhang, John R. Singler |
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| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Applied Mathematics Numerical analysis General Engineering Degrees of freedom (statistics) Boundary (topology) Numerical Analysis (math.NA) 01 natural sciences Domain (mathematical analysis) Dirichlet distribution Theoretical Computer Science 010101 applied mathematics Computational Mathematics symbols.namesake Computational Theory and Mathematics Rate of convergence Discontinuous Galerkin method FOS: Mathematics symbols Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Convection–diffusion equation Software Mathematics |
| Zdroj: | Journal of Scientific Computing. 81:623-648 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-019-01043-9 |
| Popis: | We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for the control under some assumptions on the desired state and the domain. In this work, we obtain the same convergence rate for the control using a class of embedded DG methods proposed by Nguyen, Peraire and Cockburn [J. Comput. Phys. vol. 302 (2015), pp. 674-692] for simulating fluid flows. Since the global system for embedded DG methods uses continuous elements, the number of degrees of freedom for the embedded DG methods are smaller than the HDG method, which uses discontinuous elements for the global system. Moreover, we introduce a new simpler numerical analysis technique to handle low regularity solutions of the boundary control problem. We present some numerical experiments to confirm our theoretical results. |
| Databáze: | OpenAIRE |
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