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In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schrödinger evolution equations with dynamical boundary conditions. Error estimates of optimal rates of convergence in L 2 and H 1 are proved for the accociated semidiscrete and fully discrete… (More)

We describe the joint motion of multiple kinks or interfaces for the one-dimensional Cahn-Hilliard equation on a bounded interval perturbed by small additive noise The approach is based on an approximate slow manifold, where the motion of interfaces are described by the projection onto the manifold. This was used by Bates and Xun (1994/95) to verify… (More)

Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initial-and boundary-value problem for a general Schrödin-ger-type equation posed on a two space dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a… (More)

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