Object-oriented finite element programming: I: Governing principles
Computer Methods in Applied Mechanics and Engineering
Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
Design of object oriented finite element code
Advances in Engineering Software
Strain smoothing in FEM and XFEM
Computers and Structures
Finite Element/Fictitious Domain programming for flows with particles made simple
Advances in Engineering Software
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The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.