Estimates Away From a Discontinuity for Dissipative Galerkin Methods for Hyperbolic Equations
نویسندگان
چکیده
We consider the approximate solution of the initial value problem du du , .. . . _ = _ „(*,0) = »(*), 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 the true solution u. Estimates in L^ and Lx of the pollution effects of the discontinuity are found. These estimates show those effects to decay exponentially in A"1 in regions a fixed distance d from the discontinuity and exponentially in d for fixed h.
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