Residual based a posteriori error estimators for eddy current computation
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In this article, the authors consider H (curl ; Ω)-elliptic problems that have been discretized by means of Nedelec's edge elements on tetrahedral meshes.Abstract:
We consider H (curl ;Ω)-elliptic problems that have been discretized by means of Nedelec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive refinement. Under certain assumptions on material parameters and computational domains, we derive local lower bounds and a global upper bound for the total error measured in the energy norm. The fundamental tool in the numerical analysis is a Helmholtz-type decomposition of the error into an irrotational part and a weakly solenoidal part.read more
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Journal ArticleDOI
Finite elements in computational electromagnetism
TL;DR: In this paper, finite element Galerkin schemes for a number of linear model problems in electromagnetism were discussed, and the finite element schemes were introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms.
Journal ArticleDOI
A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics
TL;DR: In this article, a three-dimensional mesh-free method for arbitrary crack initiation and propagation is proposed to ensure crack path continuity for non-linear material models and cohesive laws based on a local partition of unity.
Book ChapterDOI
Theory of adaptive finite element methods: An introduction
TL;DR: A self-contained and up-to-date discussion of AFEM for linear second order elliptic partial differential equations (PDEs) and dimension d>1, with emphasis on the differences and advantages ofAFEM over standard FEM.
Journal ArticleDOI
Equilibrated residual error estimator for edge elements
Dietrich Braess,Joachim Schöberl +1 more
TL;DR: This work simplifies and modify the equilibration of Raviart-Thomas elements such that it can be applied to the curl-curl equation and edge elements and extended in the spirit of distributions.
Journal ArticleDOI
A posteriori error estimates for Maxwell equations
TL;DR: This paper proves the reliability of a residual type a posteriori error estimator on Lipschitz domains and establishes new error estimates for the commuting quasi-interpolation operators recently introduced in J. Schoberl, Commuting quasi-intersphere operators for mixed finite elements.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
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Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
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Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
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Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems
Ernst Hairer,Gerhard Wanner +1 more
TL;DR: In this paper, the authors present the solution of stiff differential equations and differential-algebraic systems (differential equations with constraints) and discuss their application in physics, chemistry, biology, control engineering, electrical network analysis, and computer programs.