Error analysis for discontinuous Galerkin time-stepping methods for nonlinear parabolic equations via maximal regularity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917866228416512 |
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| author | Akrivis, Georgios Larsson, Stig |
| author_facet | Akrivis, Georgios Larsson, Stig |
| contents | We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error analysis in [9] for Runge-Kutta methods for nonlinear parabolic equations; in analogy to [9], the proofs are based on maximal regularity properties of discontinuous Galerkin methods for non-autonomous linear parabolic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error analysis for discontinuous Galerkin time-stepping methods for nonlinear parabolic equations via maximal regularity Akrivis, Georgios Larsson, Stig Numerical Analysis 65M12, 65M15, 65M60 We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error analysis in [9] for Runge-Kutta methods for nonlinear parabolic equations; in analogy to [9], the proofs are based on maximal regularity properties of discontinuous Galerkin methods for non-autonomous linear parabolic equations. |
| title | Error analysis for discontinuous Galerkin time-stepping methods for nonlinear parabolic equations via maximal regularity |
| topic | Numerical Analysis 65M12, 65M15, 65M60 |
| url | https://arxiv.org/abs/2412.08375 |