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However, LFA for quadratic finite element discretizations can not be performed in a standard way, since the discrete operator is defined by different stencils depending on the location of the points in the grid.
The discrete operator (M - )d, defined by.
we have: (i) The discrete operator (M - )d, defined by .
See Li [2] for further details about the elegant properties of the discrete operator.
A generalized Gâteaux derivative is introduced using a fractional discrete operator for a Jumarie fractional operator.
The discrete operator, however, need not be derived from the divergence form of the continuous equations.
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The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework.
In the second case we design discrete operators which approximate spatial derivatives of the streamfunction on irregular meshes, using discretizations of pure derivatives in the x, y and along the diagonals of the element.
Applications to Carlson's inequalities and spectral theory of discrete operators are given.
Therefore, many authors have investigated the spectral analysis of differential and discrete operators [1 10].
The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.
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