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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.08708 |
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| _version_ | 1866913834819649536 |
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| author | da Veiga, Lourenço Beirão Di Pietro, Daniele A. Haile, Kirubell B. |
| author_facet | da Veiga, Lourenço Beirão Di Pietro, Daniele A. Haile, Kirubell B. |
| contents | In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods hinges on a discontinuous Galerkin approximation of the viscous term and a reinforced upwind-type stabilization of the convective term. The derived velocity error estimates account for pre-asymptotic orders of convergence observed in convection-dominated flows through regime-dependent estimates of the error contributions. A complete set of numerical results validate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible non-Newtonian flows da Veiga, Lourenço Beirão Di Pietro, Daniele A. Haile, Kirubell B. Numerical Analysis In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods hinges on a discontinuous Galerkin approximation of the viscous term and a reinforced upwind-type stabilization of the convective term. The derived velocity error estimates account for pre-asymptotic orders of convergence observed in convection-dominated flows through regime-dependent estimates of the error contributions. A complete set of numerical results validate the theoretical findings. |
| title | A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible non-Newtonian flows |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.08708 |