Finite Element Method for First Order Hyperbolic Systems

摘要

Finite element approximations to first order hyperbolic systems of Kreiss' form usub(t) + A sub 1 usub(x) + A sub 2 u = f in a rectangular domain omega = (0,1(x)0,T)is contained in R exp 2 with mixed initial and boundary conditions u(x,0) = O, usup(I)(0,t) = alpha usup(II)(0,t), usup(II)(1,t) = beta usup(I)(1,t) are studied. The above system is transformed into a symmetric positive system of Friedrich's type Au = F in omega with admissible boundary conditions (B - M)u = 0 on delta omega . A Continuous Galerkin Approximation is then applied. When the analytical solution u is an element of (H exp 3 ( omega ) intersection Wsup(2,infinity)( omega ))sup(n) and the approximate solution usub(h), which is assumed to be the Lagrange piecewise polynomial of degree one in both variables, and when the elements of discretisation K are equal rectangles, an error estimate which is a superconvergence result is obtained. (Atomindex citation 14:747323)