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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.


References [Enhancements On Off] (What's this?)

  • [1] J. DOUGLAS, JR., T. DUPONT & J. SERRIN, "Uniqueness and comparison theorems for nonlinear elliptic equations in divergence form," Arch. Rational Mech. Anal., v. 42, 1971, pp. 157-168. MR 0393829 (52:14637)
  • [2] C. B. MORREY, JR., Multiple Integrals in the Calculus of Variations, Die Grundlehren der math. Wissenschaften, Band 130, Springer-Verlag, New York, 1966. MR 34 #2380. MR 0202511 (34:2380)
  • [3] J. A. NITSCHE, "Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die kleinen Randbedingungen unterworfen sind," Abh. Math. Sem. Univ. Hamburg, v. 36, 1970/71, pp. 9-15. MR 0341903 (49:6649)

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Additional Information

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

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