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Mathematics of Computation

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A Galerkin method for a nonlinear Dirichlet problem


Authors: Jim Douglas and Todd Dupont
Journal: Math. Comp. 29 (1975), 689-696
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1975-0431747-2
MathSciNet review: 0431747
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Abstract: A Galerkin method due to Nitsche for treating the Dirichlet problem for a linear second-order elliptic equation is extended to cover the nonlinear equation $ \nabla \cdot (a(x,u)\nabla u) = f$. The asymptotic error estimates are of the same form as in the linear case. Newton's method can be used to solve the nonlinear algebraic equations.


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DOI: https://doi.org/10.1090/S0025-5718-1975-0431747-2
Article copyright: © Copyright 1975 American Mathematical Society