Global functions

We started with local (basis) functions on finite elements. Now, we want to put them together to global functions.

We need:

• a mesh consisting of geometrical elements
• corresponding transformations from reference element to physical element
• local and global basis coefficients

We will first do this in 1D and continue with 2D afterwards.

A mesh

A mesh is a decomposition of the domain of interest into simple geometrical elements:

• line segments in 1D
• triangles (or quadrilaterals, sometimes more general polygons) in 2D
• tetrahedra, hexahedra, prisms, pyramids (sometimes more general polygons) in 3D

We will start with the simplest case: 1D domain, $(a,b) \subset \mathbb{R}$, decomposed into $N$ line segments.