Estimates Away From a Discontinuity for Dissipative Galerkin Methods for Hyperbolic Equations
Estimates Away From a Discontinuity for Dissipative Galerkin Methods for Hyperbolic Equations
We consider the approximate solution of the initial value problem \[ \frac {{\partial u}}{{\partial t}} = \frac {{\partial u}}{{\partial x}},\quad u(x,0) = v(x),\] by a dissipative Galerkin method. When v is taken to have a jump discontinuity at zero, that discontinuity will propagate along $x + t = 0$, in …