Solving the biharmonic Dirichlet problem on domains with corners |
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| Authors: | Colette De Coster Serge Nicaise Guido Sweers |
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| Affiliation: | 1. LAMAV, Université de Valenciennes et du Hainaut Cambrésis, Valenciennes Cedex 9, France;2. Mathematisches Institut der Universit?t zu K?ln, K?ln, Germany |
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| 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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| Keywords: | Biharmonic operator Corner domains 35J40 74K20 |
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