The first tutorial chapter begins with describing several mesh data formats that Hermes can read, and showing how to load, refine, and visualize meshes. Then we learn how to set up a finite element space and solve a first simple problem - a Poisson equation with zero Dirichlet boundary conditions. After that we show how to prescribe more general boundary conditions. We also explain how Hermes handles numerical quadrature since this is both very important for higher-order finite element methods and very different from standard low-order FEM codes. At the end of this chapter we will learn how to solve systems of equations and axisymmetric 3D problems.

- Finite Element Mesh (01-mesh)
- Finite Element Space (02-space)
- Poisson Equation (03-poisson)
- Model problem
- Jacobian-residual formulation
- Consistent approach to linear and nonlinear problems
- Default Jacobian for the diffusion operator
- Default residual for the diffusion operator
- Default volumetric vector form
- Selecting matrix solver
- Loading the mesh
- Performing initial mesh refinements
- Initializing the weak formulation
- Setting constant Dirichlet boundary conditions
- Initializing finite element space

- 1 - nonlinear formulation
- 2 - linear formulation
- Visualization
- Essential and Natural Boundary Conditions
- Nonconstant Dirichlet BC (04-bc-dirichlet)
- Neumann BC (05-bc-neumann)
- Newton BC (06-bc-newton)
- General 2nd-Order Linear Equation (07-general)
- Systems of Equations (08-system)
- Axisymmetric Problems (09-axisym)