An adaptive method with rigorous error control for the Hamilton–Jacobi equations. Part I: The one-dimensional steady state case

An adaptive high-order discontinuous Gal

An adaptive high-order discontinuous Galerkin method with error control for the Hamilton–Jacobi equations. Part I: The one-dimensional steady state case

✍ Yanlai Chen; Bernardo Cockburn 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 623 KB

We propose and study an adaptive version of the discontinuous Galerkin method for Hamilton-Jacobi equations. It works as follows. Given the tolerance and the degree of the polynomial of the approximate solution, the adaptive algorithm finds a mesh on which the approximate solution has an L 1 -distan