A moving Petrov‐Galerkin method for transport equations

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Abstract
A time‐dependent transport equation is solved numerically by using a Petrov‐Galerkin technique on a time‐dependent grid. A piecewise linear trial solution and piecewise Hermite cubic test functions are used. The same method is also applied to a time‐independent problem, in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid‐generation techniques. Several numerical examples are given.