A second order explicit finite element scheme to multi- dimensional conservation laws and its convergence

摘要

A second order explicit finite element scheme is given for the numerical computation to multi-dimensional scalar conservation laws. L~p-convergence to entropy solutions is proved under some usual conditions. For two-dimensional problems, uniform mesh, and sufficiently smooth solutions a second order error estimate in L~2 is proved under a stronger condition, Δt≤Ch~4/3.