A discontinuous Galerkin scheme for front propagation with obstacles (Q2436533)

The authors are interested in numerical schemes for front propagation problems that come from deterministic attainability problems, or optimal control problems. They consider the following equation \[ \min(u_t+ H(x,\nabla u),\;u-g(x))= 0,\quad x\in\mathbb{R}^d,\quad t> 0, \] together with an initial \(u(0,x)= u_0(x)\), \(x\in\mathbb{R}^d\). Here \(g(x)\) is called the ``obstacle function'' and the equation will be referred as the ``obstacle equation''. The authors propose a discontinuous Galerkin approach to solve these problems. -- Numerical results are presented.