Enhancing Biomechanical Simulations Based on a Posteriori Error Estimates: The Potential of Dual‐Weighted Residual‐Driven Adaptive Mesh Refinement
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DOI: 10.1002/cnm.3897
Abstract: The finite‐element method (FEM) is a well‐established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with a discretisation error that can be… read more here.
Keywords: posteriori error; weighted residual; error estimates; dual weighted ... See more keywords
An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems
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DOI: 10.1002/nme.5440
Abstract: Summary We propose the study of a posteriori error estimates for time–dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the… read more here.
Keywords: finite element; generalized finite; error; estimate ... See more keywords
Reduced order modeling of random linear dynamical systems based on a new a posteriori error bound
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DOI: 10.1002/nme.5942
Abstract: Reduced order models (ROMs) are becoming increasingly useful for saving computational cost in response prediction of vibrating systems. In a number of applications such as uncertainty quantification, ROMs require robustness over a wide variation of… read more here.
Keywords: error; reduced order; error bound; posteriori error ... See more keywords
A posteriori error estimates for the virtual element method
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DOI: 10.1007/s00211-017-0891-9
Abstract: An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully… read more here.
Keywords: error; element method; element; posteriori error ... See more keywords
A-posteriori error estimation for the finite point method with applications to compressible flow
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DOI: 10.1007/s00466-017-1402-7
Abstract: An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations.… read more here.
Keywords: error; compressible flow; finite point; point method ... See more keywords
A posteriori error estimates for non-stationary non-linear convection–diffusion equations
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DOI: 10.1007/s10092-018-0263-6
Abstract: Motivated by stochastic convection–diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection–diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the standard linear framework due to its… read more here.
Keywords: convection diffusion; diffusion; convection; non linear ... See more keywords
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws
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DOI: 10.1007/s10543-019-00794-z
Abstract: This article considers one-dimensional random systems of hyperbolic conservation laws. Existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws, which involve random initial data and random flux functions, are… read more here.
Keywords: error analysis; non intrusive; random; conservation laws ... See more keywords
Reliable a posteriori error estimation for state-constrained optimal control
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DOI: 10.1007/s10589-017-9908-7
Abstract: We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both… read more here.
Keywords: control; posteriori error; reliable posteriori; optimal control ... See more keywords
Asymptotically Exact Posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Nonlinear Convection–Diffusion Problems
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DOI: 10.1007/s10915-018-0687-9
Abstract: In this paper, we present and analyze implicit a posteriori error estimates for the local discontinuous Galerkin (LDG) method applied to nonlinear convection–diffusion problems in one space dimension. Optimal a priori error estimates for the… read more here.
Keywords: estimates local; error; local discontinuous; solution ... See more keywords
An Efficient DWR-Type a Posteriori Error Bound of SDFEM for Singularly Perturbed Convection–Diffusion PDEs
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DOI: 10.1007/s10915-021-01749-9
Abstract: This article deals with the residual-based a posteriori error estimation in the standard energy norm for the streamline-diffusion finite element method (SDFEM) for singularly perturbed convection–diffusion equations. The well-known dual-weighted residual (DWR) technique has been… read more here.
Keywords: error bound; posteriori error; sdfem singularly; diffusion ... See more keywords
A Posteriori Error Estimators for Fourth Order Elliptic Problems with Concentrated Loads
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DOI: 10.1007/s10915-025-03089-4
Abstract: In this paper, we study two residual-based a posteriori error estimators for the C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} interior penalty method in solving the biharmonic equation in a polygonal domain… read more here.
Keywords: posteriori error; error estimators; fourth order; order elliptic ... See more keywords