Mathematics Research Works
Permanent URI for this collectionhttp://hdl.handle.net/1903/1595
Browse
4 results
Search Results
Item Pointwise error estimates for relaxation approximations to conservation laws(Copyright: Society for Industrial and Applied Mathematics, 2000) TADMOR, EITAN; TANG, TAOWe obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip+ stability). A one-sided interpolation inequality between classical L1 error estimates and Lip+ stability bounds enables us to convert a global L1 result into a (nonoptimal) local estimate. Optimal error bounds on the weighted error then follow from the maximum principle for weakly coupled hyperbolic systems. The main difficulties in obtaining the Lip+ stability and the optimal pointwise errors are how to construct appropriate “difference functions” so that the maximum principle can be applied.Item The convergence rate of Godunov type schemes(Copyright: Society for Industrial and Applied Mathematics, 1994-02) Nessyahu, Haim; Tadmor, Eitan; Tassa, TamirItem The convergence rate of approximate solutions for nonlinear scalar conservation laws(Copyright: Society for Industrial and Applied Mathematics, 1992-12) Nessyahu, Haim; Tadmor, EitanItem Local error estimates for discontinuous solutions of nonlinear hyperbolic equations(Copyright: Society for Industrial and Applied Mathematics, 1991-08) Tadmor, Eitan