ONED
Functions for 1D Finite Elements

ONED is a MATLAB library which contains functions useful for 1D finite element calculations, by Jeff Borggaard.

Related Data and Programs:

FEM1D, a data directory which contains a description of the data files that can be used to describe a 1D finite element model.

FEM_TO_TEC, a MATLAB program which can convert an FEM model into a TEC graphics file.

FEM1D, a MATLAB program which applies the finite element method to a linear two point boundary value problem in a 1D region.

FEM1D_ADAPTIVE, a MATLAB program which applies the finite element method to a linear two point boundary value problem in a 1D region, using adaptive refinement to improve the solution.

FEM1D_DISPLAY, a MATLAB program which reads three files defining a 1D arbitrary degree finite element function, and displays a plot.

FEM1D_FUNCTION_10_DISPLAY, a MATLAB program which reads a prefix defining three finite element data files, reads the data, samples the finite element function, and displays a plot.

FEM1D_PACK, a MATLAB library which contains utilities for 1D finite element calculations.

FEM1D_PMETHOD, a MATLAB program which applies the p-method version of the finite element method to a linear two point boundary value problem in a 1D region.

FEM1D_SAMPLE, a MATLAB program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

FEM2D_PACK, a MATLAB library which contains utilities for 2D finite element calculations.

FEM3D_PACK, a MATLAB library which contains utilities for 3D finite element calculations.

OPTIMAL_CONTROL_1D, a MATLAB program which seeks the optimal control function for a one dimensional system which is represented using the finite element formulation;

PIECEWISE_LINEAR_PRODUCT_INTEGRAL, a MATLAB library which calculates the exact value of the integral of the product of two piecewise linear functions F(X) and G(X).

THREED, a MATLAB library which contains functions useful for 3D finite element calculations.

TWOD, a MATLAB library which contains functions useful for 2D finite element calculations.

Author:

Jeff Borggaard, Virginia Tech.

Source Code:

• oned_bilinear.m integrates kernel(x) * basis function(x) * test function(x).
• oned_f_int.m computes the integral of f(x) times a test function.
• oned_gauss.m sets Gauss integration points on (-1,1).
• oned_gproject.m performs Galerkin projection of a function.
• oned_mesh.m generates a mesh with a prescribed density. This routine returns elements of the same type as xb, e_connb (linear or quadratic)
• oned_plot_hermite.m, plots the Hermite shape functions.
• oned_projectd.m projects the derivative onto the continuous finite element space (this routine simply does a Galerkin projection).
• oned_shape.m computes test functions and derivatives for a Lagrange C0 element given element coordinates and Gauss points. (assumes all nodes are uniformly distributed in the element.)
• oned_shapeherm.m computes test functions and derivatives on a (C1+) Hermite element given element coordinates and Gauss points.
• oned_shapeiso.m computes test functions and derivatives for a isoparametric Lagrange C0 element given element coordinates and Gauss points.

You can go up one level to the MATLAB source codes.