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A linear implicit E...
A linear implicit Euler method for the finite element discretization of a controlled stochastic heat equation
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- Benner, Peter (författare)
- Max Planck Institute for Dynamics of Complex Technical Systems
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- Stillfjord, Tony (författare)
- Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Trautwein, Christoph (författare)
- Friedrich Schiller University Jena
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(creator_code:org_t)
- 2021-05-20
- 2022
- Engelska 33 s.
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Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press (OUP). - 0272-4979 .- 1464-3642. ; 42:3, s. 2118-2150
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Abstract
Ämnesord
Stäng
- We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with nonhomogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as well as both distributed and boundary noise. We apply the finite element method for the spatial discretization and the linear implicit Euler method for the temporal discretization. Due to the low regularity induced by the boundary noise, convergence orders above 1/2 in space and 1/4 in time cannot be expected. We prove such optimal convergence orders for our full discretization when the distributed noise and the initial condition are sufficiently smooth. Under less smooth conditions the convergence order is further decreased. Our results only assume that the related (deterministic) differential Riccati equation can be approximated with a certain convergence order, which is easy to achieve in practice. We confirm these theoretical results through a numerical experiment in a two-dimensional domain.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Convergence analysis
- Full discretization
- Heat conduction
- Optimal control
- Stochastic partial differential equation
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- art (ämneskategori)
- ref (ämneskategori)
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