A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics
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Publication:2952282
DOI10.1002/nme.4490zbMath1352.74041OpenAlexW2161623595MaRDI QIDQ2952282
José Paulo Baptista Moitinho de Almeida
Publication date: 30 December 2016
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nme.4490
verificationerror estimationerror boundsmodel reductionproper generalized decompositionlocal outputs
Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05)
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Cites Work
- On the deterministic solution of multidimensional parametric models using the proper generalized decomposition
- On the verification of model reduction methods based on the proper generalized decomposition
- A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations
- An error estimator for separated representations of highly multidimensional models
- Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation
- Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems
- A general method for recovering equilibrating element tractions
- Adaptive methods for hybrid equilibrium finite element models
- On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
- Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems
- Subdomain-based flux-free a posteriori error estimators
- The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations
- Elimination of spurious static modes in meshes of hybrid compatible triangular and tetrahedral finite elements
- Recovery of equilibrium on star patches from conforming finite elements with a linear basis
- A general degree hybrid equilibrium finite element for Kirchhoff plates
- Proper generalized decomposition of multiscale models
- The post-processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements
- The stability of stars of triangular equilibrium plate elements
- Pure equilibrium tetrahedral finite elements for global error estimation by dual analysis
- Dual adaptive finite element refinement for multiple local quantities in linear elastostatics
- Recovery of equilibrium on star patches using a partition of unity technique
- A SET OF HYBRID EQUILIBRIUM FINITE ELEMENT MODELS FOR THE ANALYSIS OF THREE-DIMENSIONAL SOLIDS
- Mastering Calculations in Linear and Nonlinear Mechanics
- Approximations in elasticity based on the concept of function space
- The Determination of Upper and Lower Bounds for the Solution of the Dirichlet Problem
- Bounds for Solutions of Boundary Value Problems in Elasticity
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