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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.18606 |
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| _version_ | 1866917282345648128 |
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| author | Pervolianakis, Christos |
| author_facet | Pervolianakis, Christos |
| contents | We consider a scalar conservation law with linear and nonlinear flux function on a bounded domain $Ω\subset{\R}^2$ with Lipschitz boundary $\partialΩ.$ We discretize the spatial variable with the standard finite element method where we use a local extremum diminishing flux limiter which is linearity preserving. For temporal discretization, we use the second order explicit strong stability preserving Runge--Kutta method. It is known that the resulting fully-discrete scheme satisfies the discrete maximum principle. Under the sufficiently regularity of the weak solution and the CFL condition $k = \mathcal{O}(h^2)$, we derive error estimates in $L^{2}-$ norm for the algebraic flux correction scheme in space and in $\ell^\infty$ in time. We also present numerical experiments that validate that the fully-discrete scheme satisfies the temporal order of convergence of the fully-discrete scheme that we proved in the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error analysis of an Algebraic Flux Correction Scheme for a nonlinear Scalar Conservation Law Using SSP-RK2 Pervolianakis, Christos Numerical Analysis 65M60, 65M15 We consider a scalar conservation law with linear and nonlinear flux function on a bounded domain $Ω\subset{\R}^2$ with Lipschitz boundary $\partialΩ.$ We discretize the spatial variable with the standard finite element method where we use a local extremum diminishing flux limiter which is linearity preserving. For temporal discretization, we use the second order explicit strong stability preserving Runge--Kutta method. It is known that the resulting fully-discrete scheme satisfies the discrete maximum principle. Under the sufficiently regularity of the weak solution and the CFL condition $k = \mathcal{O}(h^2)$, we derive error estimates in $L^{2}-$ norm for the algebraic flux correction scheme in space and in $\ell^\infty$ in time. We also present numerical experiments that validate that the fully-discrete scheme satisfies the temporal order of convergence of the fully-discrete scheme that we proved in the theoretical analysis. |
| title | Error analysis of an Algebraic Flux Correction Scheme for a nonlinear Scalar Conservation Law Using SSP-RK2 |
| topic | Numerical Analysis 65M60, 65M15 |
| url | https://arxiv.org/abs/2409.18606 |