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Solving the biharmonic Dirichlet problem on domains with corners

Abstract : The biharmonic Dirichlet boundary value problem on a bounded domain is the focus of the present paper. By Riesz’ representation theorem the existence and uniqueness of a weak solution is quite direct. The problem that we are interested in appears when one is looking for constructive approximations of a solution. Numerical methods using for example finite elements, prefer systems of second equations to fourth order problems. Ciarlet and Raviart in [7] and Monk in [21] consider approaches through second order problems assuming that the domain is smooth. We will discuss what happens when the domain has corners. Moreover, we will suggest a setting, which is in some sense between Ciarlet-Raviart and Monk, that inherits the benefits of both settings and that will give the weak solution through a system type approach.
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Submitted on : Tuesday, February 16, 2021 - 8:45:34 AM
Last modification on : Wednesday, July 6, 2022 - 3:04:26 PM

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Colette De Coster, Serge Nicaise, Guido Sweers. Solving the biharmonic Dirichlet problem on domains with corners. Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2015, 288 (8-9), pp.854-871. ⟨10.1002/mana.201400022⟩. ⟨hal-03142424⟩



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