So far we have not paid any attention to the accuracy of results. In general,
computations on a fixed mesh are not very accurate and they should not be trusted.
Controlled accuracy can be achieved through *adaptive mesh refinement (AMR)*.
Advanced adaptive higher-order FEM (*hp*-FEM) is one of the main
strengths of Hermes. With eight modes of automatic *hp*-adaptivity, Hermes
excels at delivering highly accurate results with much lower numbers of degrees
of freedom than conventional FEM codes.

- Adaptive low-order FEM and hp-FEM
- Understanding Convergence Rates
- An Introductory Example (01-intro)
- Matrix-Free Version of 01-intro
- Kelly-Based
*h*-Adaptivity (02-kelly) - Multimesh
*hp*-FEM - Adaptive Multimesh
*hp*-FEM Example (03-system) - Complex-Valued Problem (04-complex)
- Time-Harmonic Maxwell’s Equations (05-hcurl)
- Adapting Mesh to an Exact Function (06-exact)
- Newton’s Method and Adaptivity (07-nonlinear)
- Transient Problems I - Adaptivity in Space (08-transient-space-only)
- Transient Problems II - Adaptivity in Time (09-transient-time-only)
- Transient Problems III - Adaptivity in Space and Time (10-transient-space-and-time)