Search results for "analyysi"
showing 10 items of 1950 documents
Shape optimization utilizing consistent sensitivities
2010
Navier-Stokes equations
2009
GPU-accelerated time integration of Gross-Pitaevskii equation with discrete exterior calculus
2022
The quantized vortices in superfluids are modeled by the Gross-Pitaevskii equation whose numerical time integration is instrumental in the physics studies of such systems. In this paper, we present a reliable numerical method and its efficient GPU-accelerated implementation for the time integration of the three-dimensional Gross-Pitaevskii equation. The method is based on discrete exterior calculus which allows us the usage of more versatile spatial discretization than traditional finite difference and spectral methods are applicable to. We discretize the problem using six different natural crystal structures and observe the correct choices of spatial tiling to decrease the truncation error…
On a numerical solution of the Maxwell equations by discrete exterior calculus
2014
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
Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type
2018
Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mihlin--H\"ormander type and wave propagator estimates of Miyachi--Peral type for $\mathscr{L}$ cannot be wider than the corresponding ranges for the Laplace operator on $\mathbb{R}^n$. The result applies to all sub-Laplacians on Carnot groups and more general sub-Riemannian manifolds, without restrictions on the step. The proof hinges on a Fourier integral representation for the wave propagator associated with $\mathscr{L}$ and nondegeneracy properties of the sub…
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…
Assessing violence in the family : social work, courts, and discourses
2016
This article investigates social work, decision-making, and gendered violence in the family in Finland. Discourses on gendered violence in the family are compared in custody disputes, handled in district courts, and out-of-home placements, dealt with in administrative courts. Both data sets altogether include 237 cases. Proceedings in both courts share a legislative emphasis on the ‘child’s best interest’ principle, and both contexts also rely on documentation provided by social workers. The examination of the two studies is based on discourse analysis, through which we have identified hegemonic discourses that are active in both courts. The study found that violence was often disregarded o…
Opetussuunnitelman pyörteissä : ohjausryhmän sekä esi- ja alkuopetuksen niveltyöryhmän kokemuksia paikallistason opetussuunnitelmatyöstä
2016
Tutkimuksemme kohdistui paikalliseen opetussuunnitelmatyöskentelyyn sekä opetussuunnitelmauudistukseen 2016 ohjausryhmän sekä esi- ja alkuopetuksen niveltyöryhmän kokemana. Tutkimuksessa määritellään suomalaista perusopetuksen opetussuunnitelmaa käsitteenä sekä tarkastellaan suomalaista opetussuunnitelmajärjestelmää ja siihen kuuluvaa valtakunnallista ja paikallista opetussuunnitelmaa ohjaavina asiakirjoina tehtävineen, tavoitteineen ja sisältöineen. Historiallisessa katsauksessa esittelemme opetussuunnitelman ohjaavuuden ja toimivuuden muutoksia sekä tarkastelemme tutkimuskohteenamme olevan kaupungin paikallisen opetussuunnitelmatyön etenemisvaiheita. Teoreettisessa viitekehyksessä luomme …