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 O(√τ ). Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in L^1, as well as to Hamilton-Jacobi equations in C^0 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 Kruzkov. Our results provide a unified framework for existence, uniqueness and error analysis, and yield a new proof of the celebrated Crandall-Liggett error estimate.
Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications
SAVARE', GIUSEPPE
2006-01-01
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 O(√τ ). Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in L^1, as well as to Hamilton-Jacobi equations in C^0 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 Kruzkov. Our results provide a unified framework for existence, uniqueness and error analysis, and yield a new proof of the celebrated Crandall-Liggett error estimate.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
