Abstract
Nonlinear evolution equations governed by m-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order [Formula: see text]. Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in L1, as well as to Hamilton–Jacobi equations in C0 are given. The error analysis relies on a comparison principle, for the novel notion of relaxed solutions, which combines and simplifies techniques of Benilan and Kružkov. Our results provide a unified framework for existence, uniqueness and error analysis, and yield a new proof of the celebrated Crandall–Liggett error estimate.
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