Perturbed saddle-point problems in $\mathbf{L}^p$ with non-regular loads
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910049115308032 |
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| author | Alsohaim, Abeer F. Führer, Tomas Ruiz-Baier, Ricardo Villa-Fuentes, Segundo |
| author_facet | Alsohaim, Abeer F. Führer, Tomas Ruiz-Baier, Ricardo Villa-Fuentes, Segundo |
| contents | In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Clément quasi-interpolation. We take as driving example the linearised Poisson--Boltzmann (an advection-diffusion-reaction problem) in mixed form. We use perturbation arguments on the continuous and discrete levels and then derive a priori estimates that remain valid when the load that appears on the right-hand side of the "second" equation is in $\mathrm{H}^{-1}$. Further, we show a supercloseness result and {analyse convergence} of an adequate adaptation of Stenberg postprocessing for mixed advection equations with non-regular data. We provide numerical results that illustrate the convergence of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbed saddle-point problems in $\mathbf{L}^p$ with non-regular loads Alsohaim, Abeer F. Führer, Tomas Ruiz-Baier, Ricardo Villa-Fuentes, Segundo Numerical Analysis In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Clément quasi-interpolation. We take as driving example the linearised Poisson--Boltzmann (an advection-diffusion-reaction problem) in mixed form. We use perturbation arguments on the continuous and discrete levels and then derive a priori estimates that remain valid when the load that appears on the right-hand side of the "second" equation is in $\mathrm{H}^{-1}$. Further, we show a supercloseness result and {analyse convergence} of an adequate adaptation of Stenberg postprocessing for mixed advection equations with non-regular data. We provide numerical results that illustrate the convergence of the proposed scheme. |
| title | Perturbed saddle-point problems in $\mathbf{L}^p$ with non-regular loads |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.10532 |