Abstract
A numerical method for a (possibly non-convex) scalar variational problem is proposed. This method allows for computation of the Young-measure solution of the generalized relaxed version of the original problem and applies to those cases with polynomial functionals.
The Young measures involved in the relaxed problem can be represented by their algebraic moments and also a finite-element mesh is used. Eventually, thus obtained convex semidefinite program can be solved by efficient specialized mathematical-programming solvers.
This method is justified by convergence analysis and eventually tested on a 2-dimensional benchmark numerical example. It serves as an example how convex compactification can efficiently be used numerically if enough ``small'', i.e. enough coarse.