Finite element approximation for time-dependent diffusion with measure-valued source
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Date
2012-06-20
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Citation of Original Publication
Seidman, T.I., Gobbert, M.K., Trott, D.W., Kružík, Martin, Finite Element Approximation for Time-Dependent Diffusion with Measure-Valued Source, Numer. Math. (2012) 122: 709. https://doi.org/10.1007/s00211-012-0474-8
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This is a pre-print of an article published in Numerische Mathematik. The final authenticated version is available online at: https://doi.org/10.1007/s00211-012-0474-8
This is a pre-print of an article published in Numerische Mathematik. The final authenticated version is available online at: https://doi.org/10.1007/s00211-012-0474-8
Abstract
The convergence of finite element methods for elliptic and parabolic partial differential equations is well-established if source terms are sufficiently smooth. Noting that finite element computation is easily implemented even when the source terms are measure-valued—for instance, modeling point sources by Dirac delta distributions—we prove new convergence order results in two and three dimensions both for elliptic and for parabolic equations with measures as source terms. These analytical results are confirmed by numerical tests using COMSOL Multiphysics.