A second order explicit finite element scheme to multidimensional conservation laws and its convergence
Tóm tắt
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 inL
2 is proved under a stronger condition, Δt≤Ch
2/4