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A mixed finite element method for a strongly nonlinear second-order elliptic problem


Authors: F. A. Milner and E.-J. Park
Journal: Math. Comp. 64 (1995), 973-988
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1995-1303087-3
MathSciNet review: 1303087
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Abstract: The approximation of the solution of the first boundary value problem for a strongly nonlinear second-order elliptic problem in divergence form by the mixed finite element method is considered. Existence and uniqueness of the approximation are proved and optimal error estimates in $ {L^2}$ are established for both the scalar and vector functions approximated by the method. Error estimates are also derived in $ {L^q},2 \leq q \leq + \infty $.


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DOI: https://doi.org/10.1090/S0025-5718-1995-1303087-3
Keywords: Nonlinear elliptic problems, mixed finite elements, error estimates
Article copyright: © Copyright 1995 American Mathematical Society