Record link: 
http://hdl.handle.net/20.500.12708/199304
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Title: 
Optimal convergence rates in L² for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions
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Citation: 
Bernkopf, M., & Melenk, J. M. (2024). Optimal convergence rates in L2 for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions. arXiv. https://doi.org/10.48550/arXiv.2407.14424
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Publisher DOI: 
10.48550/arXiv.2407.14424
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Publication Type: 
Preprint
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Language: 
English
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Authors: 
Bernkopf, Maximilian 
Melenk, Jens Markus 
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Organisational Unit: 
E101-02-1 - Forschungsgruppe Computational Mathematics 
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ArXiv ID: 
2407.14424
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Date (published): 
19-Jul-2024
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Number of Pages: 
36
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Preprint Server: 
arXiv 
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Keywords: 
Optimal convergence rates; least squares finite element method; inhomogeneous Robin boundary conditions
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Abstract: 
We consider divergence-based high order discretizations of an L²-based first order system least squares formulation of a second order elliptic equation with Robin boundary conditions. For smooth geometries, we show optimal convergence rates in the L²(Ω) norm for the scalar variable. Convergence rates for the L²(Ω)-norm error of the gradient of the scalar variable as well as vectorial variable are also derived. Numerical examples illustrate the analysis.
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Research Areas: 
Mathematical and Algorithmic Foundations: 80%
Modeling and Simulation: 20%
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Science Branch: 
1010 - Mathematik: 100%
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