# Operator Splitting with Spatial-temporal Discretization

@article{Batkai2012OperatorSW, title={Operator Splitting with Spatial-temporal Discretization}, author={Andr'as B'atkai and Petra Csom'os and B{\'a}lint Farkas and Gregor Nickel}, journal={arXiv: Functional Analysis}, year={2012}, pages={161-171} }

Continuing earlier investigations, we analyze the convergence of operator splitting procedures combined with spatial discretization and rational approximations.

## 11 Citations

Operator splitting for dissipative delay equations

- Mathematics
- 2010

We investigate Lie–Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the…

Stability and Convergence of Product Formulas for Operator Matrices

- Mathematics
- 2012

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results…

Operator Semigroups for Convergence Analysis

- MathematicsFDM
- 2014

The paper deals with abstract Cauchy problems and presents how their solutions are approximated by using space and time discretisations and introduces and applies the basic notions of operator semigroup theory.

Unified error analysis for nonconforming space discretizations of wave-type equations

- Mathematics, Computer ScienceIMA Journal of Numerical Analysis
- 2018

A unified error analysis for nonconforming space discretizations of linear wave equations in the time domain is provided and a priori error bounds in terms of interpolation, data and conformity errors of the method are provided.

DOUGLAS–RACHFORD SPLITTING SCHEMES

- Mathematics
- 2014

Splitting methods are widely used as temporal discretizations of evolution equations. Such methods usually constitute competitive choices whenever a vector field can be split into a sum of two or…

Optimal Actuator and Observation Location for Time-Varying Systems on a Finite-Time Horizon

- Mathematics
- 2015

The choice of the location of controllers and observations is of great importance for designing control systems and improving the estimations in various practical problems. For time-varying systems…

Lie-Trotter product formula for locally equicontinuous and tight Markov semigroup

- Mathematics
- 2018

In this paper we prove a Lie-Trotter product formula for Markov semigroups in spaces of measures. We relate our results to "classical" results for strongly continuous linear semigroups on Banach…

Unified error analysis for non-conforming space discretizations of wave-type equa- tions

- Education
- 2017

Optimal Control and Observation Locations for Time-Varying Systems on a Finite-Time Horizon

- MathematicsSIAM J. Control. Optim.
- 2016

The existence and convergence of optimal locations of observations for improving the estimation of the initial state, based on the Kalman smoother, is discussed and the obtained results are applied to a linear advection-diffusion model with a special extension of emission rates.

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