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Obtaining information about pest-insect population size is an important problem of pest monitoring and control. Usually, this problem has to be solved based on scarce spatial data about the population density. The problem of monitoring can thus be linked to a more general mathematical problem of numerical integration on a coarse grid. Numerical integration… (More)

- N. B. Petrovskaya
- SIAM J. Scientific Computing
- 2006

High order discontinuous Galerkin discretization schemes are considered for steady state problems. We discuss the issue of oscillations arising when Newton’s method is employed to obtain a steady state solution. It will be demonstrated that flux approximation near flux extrema may produce spurious oscillations propagating over the domain of computation. The… (More)

- N. B. Petrovskaya
- SIAM J. Scientific Computing
- 2001

For Laplace’s equation, we discuss whether it is possible to construct a linear positive finite volume (FV) scheme on arbitrary unstructured grids. Dealing with the arbitrary grids, we state a control volume which guarantees a positive FV scheme with linear reconstruction of the solution. The control volume is defined by a property of the analytical… (More)

- A. V. Wolkov, N. B. Petrovskaya
- Computer Physics Communications
- 2010

We discuss the methodology of the validation of a higher order discontinuous Galerkin scheme for acoustic computations. That includes an accurate definition of the exact solution in the problem as well as careful study of convergence properties of a DG scheme for a chosen acoustic problem. The efficiency of a higher order scheme will be confirmed for… (More)

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