Abstract
The aim of this paper is to prove a priori error estimates for the semi-discrete solution of the dual mixed method for the heat diffusion equation in a polygonal domain. Due to the geometric singularities of the domain, the solution is not regular in the context of classical Sobolev spaces. Instead, one must use weighted Sobolev spaces. In order to recapture the optimal order of convergence, the meshes are refined in an appropriate fashion near the reentrant corners of the domain.
In memory of Günter Lumer
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Farhloul, M., Korikache, R., Paquet, L. (2007). The Dual Mixed Finite Element Method for the Heat Diffusion Equation in a Polygonal Domain, I. In: Amann, H., Arendt, W., Hieber, M., Neubrander, F.M., Nicaise, S., von Below, J. (eds) Functional Analysis and Evolution Equations. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_16
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DOI: https://doi.org/10.1007/978-3-7643-7794-6_16
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