engleski

Polynomial WENO approximation with applications

Weighted essentially non-oscillatory (WENO) procedure is used for a non– oscillatory approximation of a function. The typical WENO procedure con- structs a rational approximation of a function v(x) based on known cell aver- ages of function v(x). This approximation is essentially non-oscillatory and high order accurate for smooth enough function v(x). However, the approximating rational function obtained by the classical WENO reconstruction contains poles. Therefore, if one needs to obtain a value of function v(x) in the interior of the numerical cell, the standard WENO procedure neads special treatment to over- come instabilities that can occur. We will present a new polynomial version of the WENO procedure that provides an elegant solution to this problem by constructing an approximating polynomial that is smooth, non-oscillatory and high order accurate not only at the cell boundaries but in the entire numerical cell.

WENO; PDE; approximation

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