Abstract
A variety of Galerkin methods are studied for the parabolic equationu t =▽η(a(x)▽ u),x∈Ω⊂ℝn,t∈ (O,T], subject to the nonlinear boundary conditionu v =g(x,t,u),x∈∂Ω,t∈ (O,T] and the usual initial condition. Optimal order error estimates are derived both inL 2 (Ω) andH 1 (Ω) norms for all methods treated, including several that produce linear computational procedures.
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The authors were partially supported by The National Science Foundation during the preparation of this paper.
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Douglas, J., Dupont, T. Galerkin methods for parabolic equations with nonlinear boundary conditions. Numer. Math. 20, 213–237 (1973). https://doi.org/10.1007/BF01436565
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DOI: https://doi.org/10.1007/BF01436565