A Galerkin method for a nonlinear Dirichlet problem
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- by Jim Douglas and Todd Dupont PDF
- Math. Comp. 29 (1975), 689-696 Request permission
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.References
- Jim Douglas Jr., Todd Dupont, and James Serrin, Uniqueness and comparison theorems for nonlinear elliptic equations in divergence form, Arch. Rational Mech. Anal. 42 (1971), 157–168. MR 393829, DOI 10.1007/BF00250482
- Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511
- J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg 36 (1971), 9–15 (German). MR 341903, DOI 10.1007/BF02995904
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 689-696
- MSC: Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-1975-0431747-2
- MathSciNet review: 0431747