shape_function_derivative Function

public pure function shape_function_derivative(index, elem, s, i) result(rst)

Computes the derivative of the shape function with respect to the natural coordinate specified. The derivative is approximated centrally as $$N_{,i}(\boldsymbol{s})\approx \frac{N(\boldsymbol{s}+h\boldsymbol{e}_i)- N(\boldsymbol{s}-h\boldsymbol{e}_i)}{2h}.$$ The second derivative uses the centered finite difference $$N_{,ii}(\boldsymbol{s})\approx \frac{N(\boldsymbol{s}+h\boldsymbol{e}_i)-2N(\boldsymbol{s})+ N(\boldsymbol{s}-h\boldsymbol{e}_i)}{h^2}.$$

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int32),	intent(in)			::	index	The index of the shape function to evaluate.
class(element),	intent(in)			::	elem	The element object.
real(kind=real64),	intent(in),		dimension(:)	::	s	The natural coordinate at which to evaluate the derivative.
integer(kind=int32),	intent(in)			::	i	The index of the natural coordinate to with which the derivative is to be computed.

Return Value real(kind=real64)

The result.

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