相关论文: A goal oriented error estimator and mesh adaptivit…
The efficient and reliable approximation of convection-dominated problems continues to remain a challenging task. To overcome the difficulties associated with the discretization of convection-dominated equations, stabilization techniques…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…
We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due…
Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without spending computational effort on a dual problem. Estimates…
In the setting of multi-armed trials, adaptive designs are a popular way to increase estimation efficiency, identify optimal treatments, or maximize rewards to individuals. Recent work has considered the case of estimating the effects of K…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
A model-data inversion is applied to a very large observational dataset collected in the Southern Ocean north of the Ross Sea during late autumn to early winter, producing estimates of the frequency-dependent rate of dissipation by sea ice.…
As Arctic conditions rapidly change, human activity in the Arctic will continue to increase and so will the need for high-resolution observations of sea ice. While satellite imagery can provide high spatial resolution, it is temporally…
The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I,…
Over the past decades, several computer codes were developed for simulation and analysis of thermal-hydraulics of system behaviors in nuclear reactors under operating, abnormal transient and accident conditions. However, simulation errors…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
Robust stability of moving-horizon estimators is investigated for nonlinear discrete-time systems that are detectable in the sense of incremental input/output-to-state stability and are affected by disturbances. The estimate of a…
Calibrating simulation models that take large quantities of multi-dimensional data as input is a hard simulation optimization problem. Existing adaptive sampling strategies offer a methodological solution. However, they may not sufficiently…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
An automated algorithm to construct island divertors for stellarators is presented and is used to find divertors that meet heat flux requirements determined by engineering and material limits. The algorithm uses just two initial conditions:…
Technology of formal quantitative estimation of the conformity of the mathematical models to the available dataset is presented. Main purpose of the technology is to make easier the model selection decision-making process for the…
In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction. The a posteriori error estimator is realized using the dual-weighted residual method in which the adjoint…