Summary
We study Galerkin approximations to the solution of nonlinear Sobolev equations with homogeneous Dirichlet boundary condition in two spatial dimensions and derive optimalL 2 error estimates for the continuous Crank — Nicolson and Extrapolated Crank — Nicolson approximations.
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Lin, Y. Galerkin methods for nonlinear Sobolev equations. Aeq. Math. 40, 54–66 (1990). https://doi.org/10.1007/BF02112280
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DOI: https://doi.org/10.1007/BF02112280