  We present an adaptive multiresolution method for the numerical simulation of
ideal magnetohydrodynamics in two space dimensions. The discretization uses a
finite volume scheme based on a Cartesian mesh and an explicit compact
Rung-Kutta scheme for time integration. Harten's cell average multiresolution
allows to introduce a locally refined spatial mesh while controlling the error.
The incompressibility of the magnetic field is controlled by using a
Generalized Lagrangian Multiplier (GLM) approach with a mixed
hyperbolic-parabolic correction. Different applications to two-dimensional
problems illustrate the properties of the method. For each application CPU time
and memory savings are reported and numerical aspects of the method are
discussed. The accuracy of the adaptive computations is assessed by comparison
with reference solutions computed on a regular fine mesh.
