Publication Date:
2004
abstract:
We present a quick overview of the general problem to find 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 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.
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 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.
Iris type:
2.1 Contributo in volume (Capitolo o Saggio)
Keywords:
Gradient flows; Wasserstein distance; Dissipative evolution equations; Optimal error estimates
List of contributors:
Savare', Giuseppe
Book title:
Free Boundary Problems. Theory and Applications