Examples overview

FEAScript-core ships with Node.js examples for every model, in the examples folder. Each example is a single script that sets up a model in the five steps of your first simulation, solves it and prints the results.

These pages show, for each example, the geometry and boundary conditions, the mesh, and the results. The results were computed with FEAScript-core 0.4.0, by running the examples unchanged.

Examples

Model	Example	Mesh
Heat conduction	Wall in 1D	10 linear elements
Heat conduction	Bi-material wall in 1D	20 linear elements
Heat conduction	Fin in 2D	8 × 4 quadratic quadrilaterals
Heat conduction	Fin in 2D, Gmsh mesh	30 quadratic quadrilaterals (Gmsh)
Heat conduction	Rhomboid fin in 2D, Gmsh mesh	24 quadratic quadrilaterals (Gmsh)
Heat conduction	Fin in 2D with spatially varying k and Q	8 × 4 quadratic quadrilaterals
General-form PDE	Advection-diffusion in 1D	20 quadratic elements
General-form PDE	Nonlinear reaction-diffusion in 1D	20 linear elements
Front propagation	Solidification front in 2D	12 × 8 quadratic quadrilaterals
Creeping flow	Lid-driven cavity in 2D	12 × 6 Q2-Q1 quadrilaterals
Creeping flow	Couette flow in 2D	4 × 2 Q2-Q1 quadrilaterals
Euler–Bernoulli beam	Clamped and spring-supported beam	2 cubic Hermite elements
Euler–Bernoulli beam	Cantilever beam	4 cubic Hermite elements

Running an example

The examples import FEAScript from npm. In the folder of a model (for example examples/heatConduction), or in an empty folder with a copy of the example:

1. Create a package.json with ES module support:

   echo '{"type":"module"}' > package.json

2. Install FEAScript:

   npm install feascript

3. Run the example, for example:

   node heatConduction2DFin/heatConduction2DFin.js

The Gmsh examples read their .msh file from the folder of the script, so they can be run from any folder. Every example prints the FEAScript version first, then its results: some print the node coordinates and the solution vector, others a short summary next to the exact or published values. The command to run each example is given in its section.

How the figures were made

Geometries and meshes are drawn from the same values as the examples: the structured meshes from the mesh generator of FEAScript, the Gmsh meshes from the .msh files of the examples. The result figures show the solution that each example computes. Contour lines follow the finite element solution inside each element: the field is evaluated with the shape functions of the element on a fine grid of points, not interpolated linearly between the nodes. The highest and lowest values quoted on these pages are found the same way, so they can lie between the nodes.