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Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Tadmor, Eitan |
| Copyright Year | 1989 |
| Description | Let u(x,t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u sub epsilon(x,t) is the solution of an approximate viscosity regularization, where epsilon greater than 0 is the small viscosity amplitude. It is shown that by post-processing the small viscosity approximation u sub epsilon, pointwise values of u and its derivatives can be recovered with an error as close to epsilon as desired. The analysis relies on the adjoint problem of the forward error equation, which in this case amounts to a backward linear transport with discontinuous coefficients. The novelty of this approach is to use a (generalized) E-condition of the forward problem in order to deduce a W(exp 1,infinity) energy estimate for the discontinuous backward transport equation; this, in turn, leads one to an epsilon-uniform estimate on moments of the error u(sub epsilon) - u. This approach does not follow the characteristics and, therefore, applies mutatis mutandis to other approximate solutions such as E-difference schemes. |
| File Size | 906486 |
| Page Count | 26 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19900005531 |
| Archival Resource Key | ark:/13960/t55f3qj3n |
| Language | English |
| Publisher Date | 1989-12-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Viscosity Discontinuity Nonlinear Equations Lipschitz Condition Approximation Error Analysis Transport Properties Entropy Coefficients Estimates Conservation Laws Errors Scalars Hyperbolic Differential Equations Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
