Abstract
A general method for construction of numerical schemes for scalar conservation laws which optimizes accuracy is applied to linear advection problems and Burgers' equation. The schemes, termed accuracy optimized methods (AOMs), define and solve a quadratic programming problem at each discrete time level to minimize perturbations from higher order accurate methods subject to imposed constraints. The constraints are used to impose desired behavior on the numerical approximation of the solution of the conservation law. The resulting schemes compare favorably with other high resolution schemes for scalar conservation laws. Numerical examples are presented for linear advection of discontinuities and development and transport of shocks in Burgers' equation.
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