A decoupled Crank-Nicolson leap-frog scheme for the unsteady bioconvection flows problem with concentration dependent viscosity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917018389708800 |
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| author | Li, Chenyang |
| author_facet | Li, Chenyang |
| contents | A fully discrete Crank--Nicolson Leap--Frog (CNLF) scheme is proposed and analyzed for the unsteady bioconvection flow problem with concentration-dependent viscosity. Spatial discretization is handled via the Galerkin finite element method (FEM), while temporal discretization employs the CNLF method for the linear terms and a semi-implicit approach for the nonlinear terms. The scheme is proven to be unconditionally stable, i.e., the time step is not subject to a restrictive upper bound. Using the energy method, $L^2$-optimal error estimates are derived for the velocity and concentration . Finally, numerical experiments are presented to validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A decoupled Crank-Nicolson leap-frog scheme for the unsteady bioconvection flows problem with concentration dependent viscosity Li, Chenyang Numerical Analysis A fully discrete Crank--Nicolson Leap--Frog (CNLF) scheme is proposed and analyzed for the unsteady bioconvection flow problem with concentration-dependent viscosity. Spatial discretization is handled via the Galerkin finite element method (FEM), while temporal discretization employs the CNLF method for the linear terms and a semi-implicit approach for the nonlinear terms. The scheme is proven to be unconditionally stable, i.e., the time step is not subject to a restrictive upper bound. Using the energy method, $L^2$-optimal error estimates are derived for the velocity and concentration . Finally, numerical experiments are presented to validate the theoretical results. |
| title | A decoupled Crank-Nicolson leap-frog scheme for the unsteady bioconvection flows problem with concentration dependent viscosity |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.14034 |