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Journal articles
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.
Keywords :
Biharmonic operator
Corner domains
https://hal-uphf.archives-ouvertes.fr/hal-03142424
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Tuesday, February 16, 2021 - 8:45:34 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:16 PM
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Tuesday, February 16, 2021 - 8:45:34 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:16 PM
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