Optimal convergence rates in $L^2$ for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914904228757504 |
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| author | Bernkopf, Maximilian Melenk, Jens Markus |
| author_facet | Bernkopf, Maximilian Melenk, Jens Markus |
| contents | We consider divergence-based high order discretizations of an $L^2$-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 $L^2(Ω)$ norm for the scalar variable. Convergence rates for the $L^2(Ω)$-norm error of the gradient of the scalar variable as well as vectorial variable are also derived. Numerical examples illustrate the analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_14424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal convergence rates in $L^2$ for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions Bernkopf, Maximilian Melenk, Jens Markus Numerical Analysis 65N30, 65N35, 65N12 We consider divergence-based high order discretizations of an $L^2$-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 $L^2(Ω)$ norm for the scalar variable. Convergence rates for the $L^2(Ω)$-norm error of the gradient of the scalar variable as well as vectorial variable are also derived. Numerical examples illustrate the analysis. |
| title | Optimal convergence rates in $L^2$ for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions |
| topic | Numerical Analysis 65N30, 65N35, 65N12 |
| url | https://arxiv.org/abs/2407.14424 |