Abstract: For systems of nonlinear hyperbolic conservation laws,two adaptive discontinuous Galerkin finite element methods(ADGM) generating conforming unstructured triangular meshes are proposed.The first one is for structured mesh. It is simple and fast.The second one is for both structured and unstructured meshes.Based on posteriori error estimation of nonlinear hyperbolic conservation laws,a discontinuous interfacial mesh refinement indicator is shown in generating adaptive meshes. It is shown that the methods are flexible and reliable. Computation cost is decreased.

Key words: adaptive methods, discontinuous Galerkin finite element method, hyperbolic conservation laws