Fully discrete FEM-BEM method for a class of exterior nonlinear parabolic-elliptic problems in 2D
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Fully discrete FEM-BEM method for a class of exterior nonlinear parabolic-elliptic problems in 2DAuthor(s)
Date
2006-10Citation
M. González, Fully discrete FEM-BEM method for a class of exterior nonlinear parabolic-elliptic problems in 2D, Applied Numerical Mathematics, 56(10-11), (Oct-Nov 2006) 1340-1355.
Abstract
[Abstract] We considered a nonlinear parabolic equation in a bounded domain of R2 coupled with the Laplace equation in the corresponding exterior region. This kind of problems appears in the modelling of quasi-stationary electromagnetic fields. We chose a regular artificial boundary containing the nonlinear region in its interior. Then, we applied a symmetric FEM-BEM coupling procedure including a parameterization of the artificial boundary. We used the backward Euler method for the time discretization and an exact triangulation of the finite element domain. Assuming that the nonlinear operator is strongly monotone and Lipschitz-continuous, we proved convergence and obtained optimal error estimates for the solution of the discrete problem. Finally, we proposed a fully discrete scheme with quadrature formulas of low order and, under some additional conditions on the nonlinearity, proved that the order of convergence remains optimal.
Keywords
Parabolic–elliptic problem
Boundary elements
Finite elements
Boundary elements
Finite elements
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Rights
Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional
ISSN
0168-9274
1873-5460
1873-5460