A stabilized finite element method for a flow problem arising from 4D flow magnetic resonance imaging
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914280921628672 |
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| author | Barrenechea, Gabriel Cárcamo, Cristian Poza, Abner |
| author_facet | Barrenechea, Gabriel Cárcamo, Cristian Poza, Abner |
| contents | In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its velocity as the MRI-observed one (considered a datum) plus an ``observation error'', a modified Navier-Stokes problem is derived. This procedure allows us to estimate the quality of the measured velocity fields, while also providing an alternative approach to pressure reconstruction, thereby avoiding invasive procedures. Since equal-order approximations have become a popular choice for problems linked to pressure recovery from MRI images, we design a stabilized finite element method allowing equal-order interpolations for velocity and pressure. In the linearized version of the resulting model, we prove stability and (optimal order) error estimates and test the method with a variety of numerical experiments testing both the linearized case and the more realistic nonlinear one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A stabilized finite element method for a flow problem arising from 4D flow magnetic resonance imaging Barrenechea, Gabriel Cárcamo, Cristian Poza, Abner Numerical Analysis Analysis of PDEs 65N12, 65N15, 68U10, 76D05 In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its velocity as the MRI-observed one (considered a datum) plus an ``observation error'', a modified Navier-Stokes problem is derived. This procedure allows us to estimate the quality of the measured velocity fields, while also providing an alternative approach to pressure reconstruction, thereby avoiding invasive procedures. Since equal-order approximations have become a popular choice for problems linked to pressure recovery from MRI images, we design a stabilized finite element method allowing equal-order interpolations for velocity and pressure. In the linearized version of the resulting model, we prove stability and (optimal order) error estimates and test the method with a variety of numerical experiments testing both the linearized case and the more realistic nonlinear one. |
| title | A stabilized finite element method for a flow problem arising from 4D flow magnetic resonance imaging |
| topic | Numerical Analysis Analysis of PDEs 65N12, 65N15, 68U10, 76D05 |
| url | https://arxiv.org/abs/2601.18454 |