Numerical solution of the nonlinear heat equation in heterogeneous media. (English) Zbl 0702.65094
The nonlinear multi-dimensional heat transfer problem in discontinuously heterogeneous, but piecewise homogeneous media is treated numerically by using the enthalpy formulation, certain regularization of the contact conditions between the homogeneous subdomains, the fully implicit time discretization and linear finite elements in space with linear interpolation and numerical integration.
The convergence is proved by using a technique that does not check the time derivative of temperature. Phase transitions with a positive latent heat (i.e. Stefan problems) are covered, as well. Besides, the problem needs not be of a strongly parabolic type. Some numerical experience with the nonlinear Gauss-Seidel algorithm to solve the created nonlinear algebraic systems is presented, too.
The convergence is proved by using a technique that does not check the time derivative of temperature. Phase transitions with a positive latent heat (i.e. Stefan problems) are covered, as well. Besides, the problem needs not be of a strongly parabolic type. Some numerical experience with the nonlinear Gauss-Seidel algorithm to solve the created nonlinear algebraic systems is presented, too.
Reviewer: T.Roubíček
MSC:
| 65Z05 | Applications to the sciences |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 80A22 | Stefan problems, phase changes, etc. |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 35R35 | Free boundary problems for PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
nonlinear multi-dimensional heat transfer; enthalpy formulation; regularization; fully implicit time discretization; linear finite elements in space; convergence; Phase transitions; Stefan problems; numerical experience; nonlinear Gauss-Seidel algorithmReferences:
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