Nonlinear partial differential equations: for scientists and engineers
Nonlinear partial differential equations: for scientists and engineers
Analysis of the discontinuous Galerkin method for Hamilton—Jacobi equations
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
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A numerical scheme is proposed for a scalar two-dimensional nonlinear first-order wave equation with both continuous and piecewise continuous initial conditions. It is typical of such problems to assume formal solutions with discontinuities at unknown locations, which justifies the search for a scheme that does not rely on the regularity of the solution. To this end, an auxiliary problem which is equivalent to, but has more advantages then, the original system is formulated and shown that regularity of the solution of the auxiliary problem is higher than that of the original system. An efficient numerical algorithm based on the auxiliary problem is derived. Furthermore, some results of numerical experiments of physical interest are presented.