Mimetic (mathematics)

The goal of numerical analysis is to approximate the continuum, so instead of solving a partial differential equation one aims in solve a discrete version of the continuum problem. A numerical method is called mimetic when it mimics (or imitates) some properties of the continuum vector calculus.

So a method can be mimetic if using either finite difference or finite element method. It depends on the properties that it presents.

To be called mimetic, a numerical method should satisfy the following properties:

• a double exact sequence;
• the fundamental theorems of calculus;
• the product rule.

Examples

For example, a symplectic integrator is used to compute a numerical approximation to the ordinary differential equations that describe motion. The resulting approximation conserves energy.

A mixed finite element method applied to Darcy flows strictly conserves the mass of the flowing fluid.

See also

• Geometric integrator
• Finite element method
• Finite difference