Adaptive finite element methods for differential equations

By Wolfgang Bangerth, Rolf Rannacher. Lectures in mathematics, 2003

867 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ebe1eb076c638fe8e21183caa14870fd80523610

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Adaptive reduced basis finite element heterogeneous multiscale method (2013, methodology): “It has thus been suggested in [38, 39] to use an FE approximation of the dual problem (4.”
Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error (2007, methodology): “This classification is widely accepted and already used in textbooks on error estimation [1, 2].”
Spatial regression models over two-dimensional manifolds (2016, positive): “Secondly, the penalty term might be used to target some specific quantities of interest in accordance with a so-called goal-orientated approach [2].”
A recovery‐type error estimator for the extended finite element method based on singular+smooth stress field splitting (2008, methodology): “The error assessment tools used in finite element analysis are well known and are usually classified [9,10] into two families: residual-type error estimators and recovery-based error estimators.”
Accurate recovery-based upper error bounds for the extended finite element framework (2010, methodology): “These tools are classified [12,13] mainly into two families: residual-type error estimators and recovery-based error estimators.”
Adaptive moving mesh level set method for structure topology optimization (2008, methodology): “There have been extensive studies of the h-method and p-method, both of which have shown good efficiency for both steady-state and time-dependent problems (Bangerth and Rannacher 2003).”
AN A POSTERIORI ERROR ANALYSIS OF ADAPTIVE FINITE ELEMENT METHODS FOR DISTRIBUTED ELLIPTIC CONTROL PROBLEMS WITH CONTROL CONSTRAINTS (2008, background): “, the monographs [1,3,4,14,26,27] and the references therein).”
Estimation of interpolation error constants for the P0 and P1 triangular finite elements (2007, methodology): “Thus such an evaluation has become progressively more important and has been attempted especially for adaptive finite element calculations based on a posteriori error estimation as well as for numerical verification by FEM [1,4,6,7,13].”
An introduction to sampling via measure transport (2016, methodology): “This is in the same spirit as adjoint–based techniques in adaptive finite element methods for differential equations [7].”
Adaptive finite elements with large aspect ratio based on an anisotropic error estimator involving first order derivatives (2006, background): “Since the first paper of Babuška and Rheinboldt [9,8], a posteriori error estimates became an increasingly important aspect of the finite element method, see for instance [35,2,23,11,10] for general reviews.”
The phase field method for geometric moving interfaces and their numerical approximations (2019, neutral): “The first technique gives rise so-called residual-based error bounds [165, 307, 50, 317], and the second one is a duality-based technique, called the Dual Weighted Residual method, which leads to goal-oriented error estimates [28].”
An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation (2006, background): “In Section 6 for a stationary case we present an a posteriori error estimator, which is based on the solution of the dual variational problem [4, 5, 2].”
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity (2016, background): “Important further developments in the early stages have been accomplished in [1,43,42,28,21,9].”
Convergence Analysis of an Adaptive Finite Element Method for Distributed Control Problems with Control Constraints (2007, background): “, the monographs [1, 3, 4, 14, 25, 26] and the references therein).”