Local error estimates for adaptive mesh refinement

Fernandes, P.; Girdinio, P.; Molfino, P.; Repetto, Maurizio

doi:10.1109/20.43916

Cited by 35 publications

(17 citation statements)

References 7 publications

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“…HE STUDY of refinement criteria for adaptive FEA has been a subject of considerable importance and interest over the past decade [1], [2]. Today, the primary focus is on the research and development of effective and efficient techniques for practical 3-D applications [3]- [5].…”

mentioning

confidence: 99%

Optimal discretization based adaptive finite element analysis for electromagnetics with vector tetrahedra

Giannacopoulos

McFee

2001

IEEE Trans. Magn.

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Abstract-Efficient functional derivative formulas suitable for optimal discretization based refinement criteria are developed for 3-D adaptive finite element analysis (FEA) with vector tetrahedra. Results for generalized vector Helmholtz systems are derived directly from first principles, and confirmed numerically through fundamental benchmark evaluations. Practical adaption applications are illustrated for selected FEA refinement models.Index Terms-Adaptive systems, electromagnetic analysis, error analysis, finite element methods.

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confidence: 99%

Optimal discretization based adaptive finite element analysis for electromagnetics with vector tetrahedra

Giannacopoulos

McFee

2001

IEEE Trans. Magn.

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“…A great variety of error estimators can be found in the references. In [3]- [6], cursory reviews of the most-used estimators can be found. The most complete classification is in [7].…”

Section: Curl-recovery Error Indicatormentioning

confidence: 99%

New recovery error indicator for adaptive finite-element analysis on waveguiding structures

Díaz‐Morcillo

Balbastre

Nuño

2003

IEEE Trans. Microwave Theory Techn.

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Abstract-The adaptive finite-element method (FEM) is an iterative variant of the FEM where, in a first step, an initial mesh with few and low-order elements is generated, the corresponding algebraic problem is solved and the error in the solution is estimated in order to add degrees of freedom in those regions of the domain with the biggest error estimation. This process is repeated until an ending condition is reached. The two basic stages in this method are the error indication and the mesh enrichment. In this paper, within the analysis of waveguiding structures, a new error indicator based on the curl recovery is described. In addition, an overview on refinement techniques is presented, and the -refinement employed in this study is briefly described. Results obtained with the curl-recovery indicator are discussed and compared with the classical nonadaptive FEM and two previously developed error indicators: the residual and flux continuity indicators.

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“…Consequently, for adaptive refinement strategies applied to practical systems, it is common to estimate the solution accuracy by using a posteriori error estimators. Typically, these are either identical or closely related to the error indicators used to guide the adaptive process [1]- [4]. However, in this work, it is demonstrated that local error estimators can fail to effectively resolve the convergence properties of finite-element solutions under certain conditions.…”

mentioning

confidence: 99%

“…Consider the second-order, scalar, partial differential equation (1) in the enclosed region bounded by the surface , with boundary conditions and , where electromagnetic field unknown for which to be solved; material-related parameter equal to , , or 1; wave number of the system; source function. If the surface bounding the entire problem region is comprised of the union of the Dirichlet and Neumann surfaces, i.e.,…”

Section: Second-order Functional Derivativesmentioning

confidence: 99%

“…HE STUDY of refinement criteria for finite-element adaption in electromagnetics has been the focus of a considerable amount of work for more than a decade and is now a well-established research area [1], [2]. Today, a variety of local error indicators are used in practice for establishing reliable solution error distributions, which can then be efficiently corrected by selectively adding degrees of freedom (DOF) to regions of high relative error [3], [4].…”

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confidence: 99%

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The implications of second-order functional derivative convergence for adaptive finite-element electromagnetics

McFee

Giannacopoulos²

2002

IEEE Trans. Magn.

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Abstract-The usefulness of second-order functional derivatives for resolving convergence properties in adaptive finite-element electromagnetics is investigated. Second-order criteria are proposed to assess the convergence of the global solution for arbitrary discretizations of scalar Helmholtz systems. Effective convergence criteria are introduced and evaluated for some practical applications.Index Terms-Adaptive systems, electromagnetic analysis, error analysis, finite-element methods.

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Local error estimates for adaptive mesh refinement

Cited by 35 publications

References 7 publications

Optimal discretization based adaptive finite element analysis for electromagnetics with vector tetrahedra

Optimal discretization based adaptive finite element analysis for electromagnetics with vector tetrahedra

New recovery error indicator for adaptive finite-element analysis on waveguiding structures

The implications of second-order functional derivative convergence for adaptive finite-element electromagnetics

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