A HDG Method for Elliptic Problems with Integral Boundary Condition: Theory and Applications

Journal of Scientific Computing(2023)

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摘要
In this paper, we address the study of elliptic boundary value problems in presence of a boundary condition of integral type (IBC) where the potential is an unknown constant and the flux (the integral of the flux density) over a portion of the boundary is given by a value or a coupling condition. We first motivate our work with realistic examples from nano-electronics, high field magnets and ophthalmology. We then define a general framework stemming from the Hybridizable Discontinuous Galerkin method that accounts naturally for the IBC and we provide a complete analysis at continuous and discrete levels. The implementation in the Feel++framework is then detailed and the convergence and scalability properties are verified. Finally, numerical experiments performed on the real-life motivating applications are used to illustrate our methodology.
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关键词
Integral boundary conditions, Hybridizable Discontinuous Galerkin, 3D–0D coupling, nMOS transistor, High field magnets, Ophthalmology, 65N30, 46N40, 82D37, 82D40, 92B05
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