Convergence of a second-order linearized BDF-IPDG for nonlinear parabolic equations with discontinuous coefficients. (English) Zbl 1372.65275
The numerical discretization of two-dimensional nonlinear parabolic interface problems is considered. The diffusion coefficient is considered to be discontinuous across the interface and moreover dependent on the unknown solution. The second-order backward difference formula (BDF) is used for the time discretization and the spatial discretization is treated with the anti-symmetric interior over-penalized discontinuous Galerkin (IPDG) finite element method. The optimal-order error estimates are proven based on the assumption of piecewise regular solution. The theoretical results are supported by the numerical results.
Reviewer: Petr Sváček (Praha)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K55 | Nonlinear parabolic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
convergence; discontinuous coefficients; interior penalty; anti-symmetric; finite element; nonlinear parabolic interface problems; backward difference formula; discontinuous Galerkin finite element method; error estimates;numerical resultsReferences:
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