Local projection stabilization methods for $\boldsymbol{H}({\rm curl})$ and $\boldsymbol{H}({\rm div})$ advection problems
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908374348595200 |
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| author | Luo, Yangfan Wang, Jindong Wu, Shuonan |
| author_facet | Luo, Yangfan Wang, Jindong Wu, Shuonan |
| contents | We devise local projection stabilization (LPS) methods for advection problems in the $\boldsymbol{H}$(curl) and $\boldsymbol{H}$(div) spaces, employing conforming finite element spaces of arbitrary order within a unified framework. The key ingredient is a local inf-sup condition, enabled by enriching the approximation space with appropriate $\boldsymbol{H}$(d) bubble functions (with d = curl or div). This enrichment allows for the construction of modified interpolation operators, which are crucial for establishing optimal a priori error estimates in the energy norm. Numerical examples are presented to verify both the theoretical results and the stabilization properties of the proposed method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local projection stabilization methods for $\boldsymbol{H}({\rm curl})$ and $\boldsymbol{H}({\rm div})$ advection problems Luo, Yangfan Wang, Jindong Wu, Shuonan Numerical Analysis 65N60, 65N12 We devise local projection stabilization (LPS) methods for advection problems in the $\boldsymbol{H}$(curl) and $\boldsymbol{H}$(div) spaces, employing conforming finite element spaces of arbitrary order within a unified framework. The key ingredient is a local inf-sup condition, enabled by enriching the approximation space with appropriate $\boldsymbol{H}$(d) bubble functions (with d = curl or div). This enrichment allows for the construction of modified interpolation operators, which are crucial for establishing optimal a priori error estimates in the energy norm. Numerical examples are presented to verify both the theoretical results and the stabilization properties of the proposed method. |
| title | Local projection stabilization methods for $\boldsymbol{H}({\rm curl})$ and $\boldsymbol{H}({\rm div})$ advection problems |
| topic | Numerical Analysis 65N60, 65N12 |
| url | https://arxiv.org/abs/2505.16468 |