Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition (Q2781506)
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scientific article; zbMATH DE number 1721507
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition |
scientific article; zbMATH DE number 1721507 |
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Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition (English)
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20 March 2002
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nonlinear elliptic boundar value problem
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error estimates
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nonstandard boundary conditions
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linearization
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convergence
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numerical examples
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The author develops a robust and efficient linearization algorithm for nonlinear elliptic second-order boundary value problems with mixed boundary conditions, including some nonstandard nonlocal conditions. The nonlinearity can appear as a source term or at Robin type boundary condition, are monotonically increasing and globally Lipschitz continuous and may degenerate at certain points. The author proves error estimates in several norms for the iterative scheme which converges for arbitrary starting points. This is illustrated for a numerical example on the unit square.
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