Abstract
We present a quick overview of the general problem of finding optimal a priori and a posteriori error estimates for the approximation of dissipative evolution equations in Hilbert and metric spaces by means of a variational formulation of the implicit Euler scheme. We shall discuss what are the intrinsic metric arguments which are involved in the derivation of the estimates and we will present an elementary proof in a simplified finite dimensional case. An application to the porous medium equation in the new framework of the Wasserstein distance is briefly sketched.
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Savaré, G. (2003). Error Estimates for Dissipative Evolution Problems. In: Colli, P., Verdi, C., Visintin, A. (eds) Free Boundary Problems. ISNM International Series of Numerical Mathematics, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7893-7_22
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DOI: https://doi.org/10.1007/978-3-0348-7893-7_22
Publisher Name: Birkhäuser, Basel
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