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Numerical tests justify that this method achieves fully second-order accuracy in both the temporal variable and vertical coordinate.
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The temporal variable \(t\) is fixed here.
Points in B are denoted by (x_{j}) and (tin [0,infty)) is the temporal variable.
The method uses a convexity-splitting scheme to discretize in the temporal variable and a nonconforming finite element method to discretize in the spatial variable.
In the first one, we give explicit solutions which are independent of the space variable x or the temporal variable t.
where, for the sake of simplicity, we have dropped the temporal variable and have set the horizontal and vertical inter-sensor distances equal to d.
(112) Then the function v defined by v x,t)=tilde{h}(x),quad xgeq0, tgeq0 (113) is a solution to Problem P̃ independent of the temporal variable t. .
Points in B are denoted by x j and t ∈ [ 0, ∞ ) is the temporal variable. Throughout this work the Einstein summation convention over repeated indices is used.
The solution is developed in the context of a classic weighted-residual method, where the temporal variable is treated in an elliptic fashion.
For the temporal variable, the ITI between targets varied.
Reverting back to the temporal variable t, we obtain Eqs.
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