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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


A Galerkin method for a nonlinear Dirichlet problem

Authors: Jim Douglas and Todd Dupont
Journal: Math. Comp. 29 (1975), 689-696
MSC: Primary 65N30
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] 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 0393829 (52 #14637)
  • [2] 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 (34 #2380)
  • [3] 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). Collection of articles dedicated to Lothar Collatz on his sixtieth birthday. MR 0341903 (49 #6649)

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PII: S 0025-5718(1975)0431747-2
Article copyright: © Copyright 1975 American Mathematical Society