A space-time finite element method for parabolic obstacle problems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913728724729856 |
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| author | Carvajal, José Joaquín Damircheli, Davood Führer, Thomas Fuica, Francisco Karkulik, Michael |
| author_facet | Carvajal, José Joaquín Damircheli, Davood Führer, Thomas Fuica, Francisco Karkulik, Michael |
| contents | We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on simplicial and prismatic meshes are studied and we show a priori error estimates for both. Convergence rates are derived for sufficiently smooth solutions. Reliable a posteriori bounds are provided and used to steer an adaptive algorithm. Numerical experiments including a one-phase Stefan problem and an American option pricing problem are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A space-time finite element method for parabolic obstacle problems Carvajal, José Joaquín Damircheli, Davood Führer, Thomas Fuica, Francisco Karkulik, Michael Numerical Analysis 49J40, 58E35, 65N12, 65N30 We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on simplicial and prismatic meshes are studied and we show a priori error estimates for both. Convergence rates are derived for sufficiently smooth solutions. Reliable a posteriori bounds are provided and used to steer an adaptive algorithm. Numerical experiments including a one-phase Stefan problem and an American option pricing problem are presented. |
| title | A space-time finite element method for parabolic obstacle problems |
| topic | Numerical Analysis 49J40, 58E35, 65N12, 65N30 |
| url | https://arxiv.org/abs/2503.07808 |