Category: Finite element method

Infinite element method
The infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The method divides the domain concerned i
Surface triangulation
Triangulation of a surface means * a net of triangles, which covers a given surface partly or totally, or * the procedure of generating the points and triangles of such a net of triangles.
Flexibility method
In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its
Marine Unsaturated Model
The Marine Unsaturated Model (MARUN model) is a two-dimensional (vertical slice) finite element model capable of simulating the migration of water and solutes in saturated-unsaturated porous media whi
Multiphase topology optimisation
The Multi Phase Topology Optimisation is a simulation technique based on the principle of the finite element method which is able to determine the optimal distribution of two or more different materia
Discontinuous Galerkin method
In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite vol
VisualFEA is a finite element analysis software program for Microsoft Windows and Mac OS X. It is developed and distributed by Intuition Software, Inc. of South Korea, and used chiefly for structural
Raviart–Thomas basis functions
In applied mathematics, Raviart–Thomas basis functions are vector basis functions used in finite element and boundary element methods. They are regularly used as basis functions when working in electr
Spectral element method
In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewi
Guyan reduction
In computational mechanics, Guyan reduction, also known as static condensation, is a dimensionality reduction method which reduces the number of degrees of freedom by ignoring the inertial terms of th
Finite element machine
The Finite Element Machine (FEM) was a late 1970s-early 1980s NASA project to build and evaluate the performance of a parallel computer for structural analysis. The FEM was completed and successfully
Loubignac iteration
In applied mathematics, Loubignac iteration is an iterative method in finite element methods. It gives continuous stress field. It is named after Gilles Loubignac, who published the method in 1977.
Streamline upwind Petrov–Galerkin pressure-stabilizing Petrov–Galerkin formulation for incompressible Navier–Stokes equations
The streamline upwind Petrov–Galerkin pressure-stabilizing Petrov–Galerkin formulation for incompressible Navier–Stokes equations can be used for finite element computations of high Reynolds number in
Hermes Project
Hermes2D (Higher-order modular finite element system) is a C++/Python library of algorithms for rapid development of adaptive hp-FEM solvers. hp-FEM is a modern version of the finite element method (F
Hu–Washizu principle
In continuum mechanics, and in particular in finite element analysis, the Hu–Washizu principle is a variational principle which says that the action is stationary, where is the elastic stiffness tenso
Wood–Armer method
The Wood–Armer method is a structural analysis method based on finite element analysis used to design the reinforcement for concrete slabs. This method provides simple equations to design a concrete s
Flexcom is a finite element analysis software package used in the offshore oil and gas and marine renewable energy industries. An educational version is also available for universities.
Spatial twist continuum
In finite element analysis, the spatial twist continuum (STC) is a dual representation of a hexahedral mesh that defines the global connectivity constraint. Generation of an STC can simplify the autom
Finite element method in structural mechanics
The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems
Modal analysis using FEM
The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. It is common to use the finite element metho
SAMCEF is a finite element analysis (FEA) software package dedicated to mechanical virtual prototyping. SAMCEF development started in 1965 at the Aerospace Laboratory of University of Liège. It was de
Motz's problem
In mathematics, Motz's problem is a problem which is widely employed as a benchmark for singularity problems to compare the effectiveness of numerical methods. The problem was first presented in 1947
A superelement is a finite element method technique which consists of defining a new type of finite element by grouping and processing a set of finite elements. A superelement describes a part of a pr
hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations that employs elements of vari
MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and
Bridge Software Institute
The Bridge Software Institute is headquartered at the University of Florida (UF) in Gainesville, Florida. It was established in January 2000 to oversee the development of bridge related software produ
In numerical analysis, a superconvergent or supraconvergent method is one which converges faster than generally expected (superconvergence or supraconvergence). For example, in the Finite Element Meth
Finite element updating
Finite element model updating is the process of ensuring that finite element analysis results in models that better reflect the measured data than the initial models. It is part of verification and va
Dynamic design analysis method
The dynamic design analysis method (DDAM) is a US Navy-developed analytical procedure for evaluating the design of equipment subject to dynamic loading caused by underwater explosions (UNDEX). The ana
p-FEM or the p-version of the finite element method is a numerical method for solving partial differential equations. It is a discretization strategy in which the finite element mesh is fixed and the
Patch test (finite elements)
The patch test in the finite element method is a simple indicator of the quality of a finite element, developed by Bruce Irons.The patch test uses a partial differential equation on a domain consistin
Interval finite element
In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be applied in situations where it is not possible to
Grid classification
Grid or mesh is defined as smaller shapes formed after discretisation of geometric domain. Mesh or grid can be in 3- dimension and 2-dimension. Meshing has applications in the fields of geography, des
Smoothed finite element method
Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed by combining meshfree methods with the fini
Finite element method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the tradi
Proper orthogonal decomposition
The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational fluid dynamics and structural analysis (lik
Vflo is a commercially available, physics-based distributed hydrologic model generated by Vieux & Associates, Inc. Vflo uses radar rainfall data for hydrologic input to simulate distributed runoff. Vf
Extended finite element method
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite eleme
Discrete exterior calculus
In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs and finite element meshes. DEC methods have proved to be very powerfu
Isogeometric analysis
Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. Currently, it is necessary to
Barsoum elements
Barsoum elements is a finite element analysis technique used in fracture analysis to determine the stress intensity factor of a crack. It was introduced by R. Barsoum in 1976.
Functionally graded element
In materials science and mathematics, functionally graded elements are elements used in finite element analysis. They can be used to describe a functionally graded material.
Bramble–Hilbert lemma
In mathematics, particularly numerical analysis, the Bramble–Hilbert lemma, named after James H. Bramble and Stephen Hilbert, bounds the error of an approximation of a function by a polynomial of orde
Finite element exterior calculus
Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application has been a comprehensive theory for finite elemen
Mixed finite element method
In numerical analysis, the mixed finite element method, is a type of finite element method in which extra fields to be solved are introduced during the posing a partial differential equation problem.