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- W4245760166 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=nabla dot left-parenthesis a left-parenthesis x comma u right-parenthesis nabla u right-parenthesis equals f> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:mo>⋅<!-- ⋅ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>nabla cdot (a(x,u)nabla u) = f</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. 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." @default.
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- W4245760166 date "1975-01-01" @default.
- W4245760166 modified "2023-10-18" @default.
- W4245760166 title "A Galerkin method for a nonlinear Dirichlet problem" @default.
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- W4245760166 doi "https://doi.org/10.1090/s0025-5718-1975-0431747-2" @default.
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