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The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure.
As a demonstrative example, the discrete weak gradient operator is employed as a building block in the design of numerical schemes for a second order elliptic problem, in which the classical gradient operator is replaced by the discrete weak gradient.
Hence, a thresholding coefficient K allows to distinguish between the zones with large gradient values and those with weak gradient ones.
The weak gradient between 0 and 150 m Alt for all three tree species seems plausible, because it can be assumed that the growth conditions at these altitudes are relatively uniform, if all other influence factors are constant.
There is a persistent, although weak, gradient in temperature along the West Iberian coast, with yearly-averaged sea surface temperature in the North coast of Portugal 2 3°C lower than in the Central coast [37].
Maternal alcohol consumption demonstrates a weak gradient effect.
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The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients.
These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation.
The use of weak gradients and their approximations results in a new concept called discrete weak gradients which is expected to play an important role in numerical methods for partial differential equations.
The symbol (H^{1} ({mathrm{D}_{mathrm{F}}} )) denotes the Sobolev space of the real-valued functions on (mathrm{D_{mathrm{F}}}) with square integrable weak gradients.
The discrete weak gradients of these constant basis functions are specified in local Raviart Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals.
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