The Discontinuous Enrichment Method
TLDR
A finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it is proposed, expected to attain high coarse-mesh accuracy without significant degradation of conditioning.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2000-08-16 and is currently open access. It has received 376 citations till now. The article focuses on the topics: Mixed finite element method & Finite element method.read more
Citations
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The extended/generalized finite element method: An overview of the method and its applications
TL;DR: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented in this article, which enables accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements.
Journal ArticleDOI
A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
TL;DR: Preliminary results obtained for two-dimensional model problems discretized by uniform meshes reveal that the proposed DGM enables the development of elements that are far more competitive than both the standard linear and the standard quadratic Galerkin elements for the discretization of Helmholtz problems.
Reference EntryDOI
Multiscale and Stabilized Methods
TL;DR: A general treatment of the variational multiscale method in the context of an abstract Dirichlet problem is then presented which is applicable to advective-diffusive processes and other processes of physical interest as mentioned in this paper.
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Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments
Wei Zeng,Gui-Rong Liu +1 more
TL;DR: The smoothed finite element methods (S-FEM) as discussed by the authors are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the mesh free methods.
Journal ArticleDOI
Fast integration and weight function blending in the extended finite element method
TL;DR: Two issues in the extended finite element method (XFEM) are addressed: efficient numerical integration of the weak form when the enrichment function is self‐equilibrating and blending of the enrichment.
References
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Book
Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
Journal ArticleDOI
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.
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The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
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The Partition of Unity Method
Ivo Babuška,Jens Markus Melenk +1 more
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
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The partition of unity finite element method: Basic theory and applications
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