A posteriori analysis for nonlinear convection-diffusion systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917003277631488 |
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| author | Dedner, Andreas Giesselmann, Jan Kwon, Kiwoong Pryer, Tristan |
| author_facet | Dedner, Andreas Giesselmann, Jan Kwon, Kiwoong Pryer, Tristan |
| contents | This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated and degenerate parabolic problems. Our a posteriori error bounds are valid for a family of discontinuous Galerkin spatial discretizations and various temporal discretizations that include explicit and implicit-explicit time-stepping schemes, popular tools for practical simulations of this class of problem. We prove that our estimators provide reliable upper bounds for the error of the numerical method and present numerical evidence showing that they achieve the same order of convergence as the error. Since one of our main interests is the convection dominant case, we also track the dependence of the estimator on the viscosity coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A posteriori analysis for nonlinear convection-diffusion systems Dedner, Andreas Giesselmann, Jan Kwon, Kiwoong Pryer, Tristan Numerical Analysis Analysis of PDEs 65M15, 65M60, 35L65, 35K65 This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated and degenerate parabolic problems. Our a posteriori error bounds are valid for a family of discontinuous Galerkin spatial discretizations and various temporal discretizations that include explicit and implicit-explicit time-stepping schemes, popular tools for practical simulations of this class of problem. We prove that our estimators provide reliable upper bounds for the error of the numerical method and present numerical evidence showing that they achieve the same order of convergence as the error. Since one of our main interests is the convection dominant case, we also track the dependence of the estimator on the viscosity coefficient. |
| title | A posteriori analysis for nonlinear convection-diffusion systems |
| topic | Numerical Analysis Analysis of PDEs 65M15, 65M60, 35L65, 35K65 |
| url | https://arxiv.org/abs/2510.09449 |