This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient...
This paper presents the numerical analysis for a
variational formulation of rate-independent phase transformations
in elastic solids due to Mielke The new model itself
suggests an implicit time-discretization which is combined with the
finite element method in space.
error estimates are established for the
quasioptimal spatial approximation of the stress field
within one time-step.
error estimates motivate an
adaptive mesh-refining algorithm for efficient discretization.
The proposed...
The primary objective of this work is to develop coarse-graining
schemes for stochastic many-body microscopic models and quantify their
effectiveness in terms of and error analysis. In
this paper we focus on stochastic lattice systems of
interacting particles at equilibrium.
The proposed algorithms are derived from an initial coarse-grained
approximation that is directly computable by Monte Carlo simulations,
and the corresponding numerical error is calculated using the specific relative entropy...
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