Search results for "Estimates"
showing 10 items of 72 documents
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
2020
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…
Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
2018
We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems
2019
The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Furthermore, a p…
Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems
2018
The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example. peerReviewed
A posteriori error estimates for variational problems in the theory of viscous fluids
2016
The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham problem. In the summary of the thesis we consider only the Oseen problem. The papers present and justify special forms of these estimates which are suitable for the approximations generated by the Uzawa algorithm. The estimates are of two main types. Estimates of the first type use exact solutions obtained on the steps of the Uzawa algorithm. They show how errors encompassed in Uzawa approximations behave and have mainly theoretical meaning. Estimates of the second type o…
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
Residual a posteriori error estimation for frictional contact with Nitsche method
2023
We consider frictional contact problems in small strain elasticity discretized with finite elements and Nitsche method. Both bilateral and unilateral contact problems are taken into account, as well as both Tresca and Coulomb models for the friction. We derive residual a posteriori error estimates for each friction model, following [Chouly et al, IMA J. Numer. Anal. (38) 2018, pp. 921-954]. For the incomplete variant of Nitsche, we prove an upper bound for the dual norm of the residual, for Tresca and Coulomb friction, without any extra regularity and without a saturation assumption. Numerical experiments allow to assess the accuracy of the estimates and their interest for adaptive meshing …
Gaussian processes retrieval of crop traits in Google Earth Engine based on Sentinel-2 top-of-atmosphere data.
2022
The unprecedented availability of optical satellite data in cloud-based computing platforms, such as Google Earth Engine (GEE), opens new possibilities to develop crop trait retrieval models from the local to the planetary scale. Hybrid retrieval models are of interest to run in these platforms as they combine the advantages of physically-based radiative transfer models (RTM) with the flexibility of machine learning regression algorithms. Previous research with GEE primarily relied on processing bottom-of-atmosphere (BOA) reflectance data, which requires atmospheric correction. In the present study, we implemented hybrid models directly into GEE for processing Sentinel-2 (S2) Level-1C (L1C)…
Hölder regularity for stochastic processes with bounded and measurable increments
2022
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.