Adaptive finite element methods
Parallel multigrid on unstructured grids using adaptive finite element methods
... In t his method the number of nodes per processor sti ll decreases as we move down t he levels, but t he fine grid relaxation sweeps may be performed in parallel with the coarse grid cor[r] ...
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An hp adaptive Newton discontinuous Galerkin finite element approach for semilinear elliptic boundary value problems
... of adaptive finite element methods, for example, is to first discretise the underlying PDE problem, in our case (1), and to derive an a posteriori error bound for the resulting (nonlinear) ...
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Adaptive fully-discrete finite element methods for nonlinear quadratic parabolic boundary optimal control
... study adaptive fully-discrete finite element methods for quadratic boundary optimal control problems governed by nonlinear parabolic ...reliable adaptive finite element approximation for ...
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Finite Element Simulations of Shape Memory Alloy Actuators in Adaptive Structures
... an adaptive structure, and where the driving frequency is significantly smaller that the structural natural frequency, the hysteresis acts as an impediment in the ability of conventional control methods to ...
107
A posteriori error estimation for a PDE constrained optimization problem involving the generalized Oseen equations
... In the current work, the assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard ...
35
On the adaptive selection of the parameter in stabilized finite element approximations
... such methods are available in the literature (see [20, 10] for extensive ...the element level or can simply be based on compensating for the inf-sup deficiency of the ...finite element methods, ...
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Adaptive Finite Element Modeling of Fatigue Crack Propagation
... several methods use to predict the direction of crack trajectory such as the maximum circumferential stress theory, the maximum energy release rate theory and the minimum strain energy density ...
5
Fast Finite Element Method Using Multi-Step Mesh Process
... optimizing methods, for example Wavelet transform, concentrate just on matrix equation and optimizing the solution ...optimization methods is that their efficiency is correlated with the matrix ...these ...
9
An adaptive stabilized finite element method for the generalized Stokes problem
... [20,21] and Bank and Welfert [7], laid the basic foundation for the mathe- matical analysis of practical methods (see also [11] for error estimators in the nonconforming case). More recently, in [3,2] and [12], a ...
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An adaptive finite element approximation of a variational model of brittle fracture
... numerical methods, which we describe in sections 2–5, we will be pragmatic regarding this point and will not make the distinction between local and global ...
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Finite element methods: Research in India over the last decade
... and adaptive FEM for conforming, nonconforming and DG FEMs for the von K´arm´an equations that allows reliable and efficient error control has also been ...
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hp Adaptive discontinuous Galerkin methods for neutron transport criticality problems
... error estimator we have designed and implemented both h- and hp-refinement strate- gies, which are capable of automatically refining the finite element spaces employed within both the spatial and angular ...
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An adaptive finite element approximation of a generalized Ambrosio Tortorelli functional
... numerical methods in the literature that are based on minimizing an approximation of the energy functional E(u, Γ), which is able to represent the crack set in a manner more readily tractable by numerical ...
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On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems
... To the best of our knowledge, three classes of convergence proofs for adaptive finite element methods for linear problems exist to date. The first idea [19, 23] used the so-called inner node property ...
23
Software for finite element methods and its application to nonvariational problems
... numerical methods that target this problem are relatively ...numerical methods developed for tackling nonvariational problems were finite difference methods ...
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Consistent local projection stabilized finite element methods
... projection methods inside an enriching frame- work relied on ...projection methods) and still maintain them parameter-free, and without the need of a dual coarser mesh satisfying a macro-element ...
28
Discontinuous Galerkin Finite Element Methods for Photonic Crystals
... The finite element toolkit hpGEM [30] has been used to construct the matrices in the DG discretisation. It is a DGFEM package developed by the MACS chair at the University of Twente. It provides routines ...
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Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method
... of finite element methods (FEM) [17], as it utilizes finite element, namely, localized basis functions which can become infinitely small when the grid size of the computation window is ...
11
Finite Element Methods for Interface Problems with Locally Modified Triangulations
... numerical methods designed for smooth solutions do not work efficiently for in- terface ...the finite element method (FEM) with a body-fitted ...to finite difference methods, which ...
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Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes
... The objective of this paper is to propose and analyse a stabilised finite element method for the Oseen problem on anisotropic quadrilateral meshes containing corner patches. The stabilisation terms related ...
29