One-Step Collocation: Uniform Superconvergence, Predictor-Corrector Method, Local Error Estimate

1985 ◽  
Vol 22 (6) ◽  
pp. 1135-1152 ◽  
Author(s):  
Marino Zennaro
Keyword(s):  
Error Estimate ◽  
Local Error ◽  
One Step ◽  
Predictor Corrector ◽  
Local Error Estimate

Kriging regression of PIV data using a local error estimate

2014 ◽  
Vol 55 (1) ◽  
Author(s):  
Jouke H. S. de Baar ◽  
Mustafa Percin ◽  
Richard P. Dwight ◽  
Bas W. van Oudheusden ◽  
Hester Bijl
Keyword(s):  
Error Estimate ◽  
Local Error ◽  
Local Error Estimate

scholarly journals A Predictor-Corrector Method for Solving Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zong-Ke Bao ◽  
Ming Huang ◽  
Xi-Qiang Xia
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Auxiliary Problem ◽  
The Other ◽  
Stationary Points ◽  
Stopping Criterion ◽  
Auxiliary Problem Principle ◽  
One Step ◽  
Predictor Corrector

We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise toΔ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.

scholarly journals Goal Oriented Time Adaptivity Using Local Error Estimates

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 113
Author(s):  
Peter Meisrimel ◽  
Philipp Birken
Keyword(s):  
Error Estimates ◽  
Initial Value Problems ◽  
Error Propagation ◽  
Adaptive Methods ◽  
Local Error ◽  
A Posteriori ◽  
Initial Value ◽  
Numerical Tests ◽  
Performance Predictions ◽  
Local Error Estimate

We consider initial value problems (IVPs) where we are interested in a quantity of interest (QoI) that is the integral in time of a functional of the solution. For these, we analyze goal oriented time adaptive methods that use only local error estimates. A local error estimate and timestep controller for step-wise contributions to the QoI are derived. We prove convergence of the error in the QoI for tolerance to zero under a controllability assumption. By analyzing global error propagation with respect to the QoI, we can identify possible issues and make performance predictions. Numerical tests verify these results. We compare performance with classical local error based time-adaptivity and a posteriori based adaptivity using the dual-weighted residual (DWR) method. For dissipative problems, local error based methods show better performance than DWR and the goal oriented method shows good results in most examples, with significant speedups in some cases.

scholarly journals Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices

2010 ◽  
Vol 17 (4-5) ◽  
pp. 397-405
Author(s):  
U. Miller ◽  
S. Bograd ◽  
A. Schmidt ◽  
L. Gaul
Keyword(s):  
Rayleigh Quotient ◽  
Damping Factor ◽  
Metallic Structures ◽  
Finite Element Software ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Symmetric Complex ◽  
One Step ◽  
Predictor Corrector ◽  
Complex Valued

A vibration analysis of a structure with joints is performed. The simulation is conducted with finite element software capable of performing a numeric modal analysis with hysteretic damping assumption. The joints are modeled with thin layer elements, representing dissipation and stiffness of the joints. The matrices describing the system consist of the mass, as well as real and complex-valued stiffness matrices. If the eigenvalues of this system are found in one step, due to the mode crossing occurring for the closely spaced modes, it is difficult and time consuming to assign calculated modal damping factors to the corresponding undamped eigenvalues. In order to avoid this problem, an eigenvalue following method is used. The outcome of the solution is the graphical presentation of continuous eigenvalue paths, showing the change in the eigenvalues from the undamped to the fully damped case. For every undamped eigenvalue exists its equivalent eigenfrequency and damping factor that can be used for further numerical analysis.In scope of this article a Predictor-Corrector and a Rayleigh-Quotient Iteration algorithms are applied to the problem. The algorithms are tested specifically on the type of matrices resulting from the weakly damped hysteretic formulation arising from the simulation of metallic structures with joints.

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