Tutorial Guide

These tutorials are designed to help users of the puncturedfem package become acquainted with some of its features, and how to avoid some potential pitfalls.

Note: The tutorials are still under construction; be sure to check back in the future!

The tutorials are partitioned into four chapters, each with a different focus.

Chapter 1. Mesh Geometry

This chapter is devoted to building curvilinear and punctured meshes, which is somewhat more involved than conventional triangulations.

• 1.1: Vertices and Edges
• 1.2: Mesh Construction

Chapter 2. Local Poisson Spaces

This chapter explores the local Poisson space \(V_p(K)\), which will be used to construct a finite element problem in Chapter 3.

• 2.1: Polynomials
• 2.2: Dirichlet Traces
• 2.3: Local Poisson Functions
• 2.4: Local Poisson Spaces

Chapter 3. Finite Elements with Poisson Spaces

This chapter introduces global Poisson spaces, and how they can be used in finite element methods.

• 3.1: Global Poisson Spaces
• 3.2: Global Boundary Conditions

Chapter 4.Advanced Features

This chapter covers some features that not all users are likely to need, but may be important in some situations.

• 4.1: Nyström Solvers
• 4.2: Heavy Sampling of an Intricate Edge