Backward Euler discretization of fully nonlinear parabolic problems

González, C.; Ostermann, A.; Palencia, C.; Thalhammer, M.

doi:10.1090/S0025-5718-01-01330-8

Backward Euler discretization of fully nonlinear parabolic problems
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by C. González, A. Ostermann, C. Palencia and M. Thalhammer PDF

Math. Comp. 71 (2002), 125-145 Request permission

Abstract:

This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further show that the geometric properties near a hyperbolic equilibrium are well captured by the discretization. A numerical example is given.

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