High order regularity for solutions of the inviscid burgers equation
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We discuss a recent Besov space regularity theory for discontinuous, entropy solutions of quasilinear, scalar hyperbolic conservation laws in one space dimension. This theory is very closely related to rates of approximation in L1 by moving grid, finite element methods. In addition, we establish the Besov space regularity of solutions of the inviscid Burgers equation; the new aspect of this study is that no assumption is made about the local variation of the initial data.
KeywordsBesov Space Algebraic Curf Entropy Solution Piecewise Polynomial Springer Lecture Note
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- R. A. DeVore and B. J. Lucier, High order regularity for conservation laws, Purdue University Center for Applied Mathematics, Tech. Rep. 85, Aug. 1988.Google Scholar
- J. Glimm, B. Lindquist, O. McBryan, and L. Padmanabhan, A front tracking reservoir simulator, five-spot validation studies and the water coning problem, in Mathematics of Reservoir Simulation, R. E. Ewing, ed., SIAM, Philadelphia, 1983.Google Scholar
- K. Miller, Alternate modes to control the nodes in the moving finite element method, in Adaptive Computational Methods for Partial Differential Equations, I. Babuska, J. Chandra, J. Flaherty, ed., SIAM, Philadelphia, 1983.Google Scholar