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The rest of the paper is organized as follows: In Section 2, we first propose the novel stabilized method which uses only one stabilization parameter.
The stabilized method is based on the algebraic version of the sub-grid scale approach.
The stabilized method is designed by adding a jump term of the discrete pressure to the continuity approximation equation.
A stabilized method is designed to improve the accuracy of t⁎ by statistically selecting the optimum frequency band for regression.
In particular, we have designed a new stabilized method that allows the use of piecewise constant pressures.
For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge Kutta ("SDIRK -) method.
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This model involves a characteristic length scale, that can go from the element size to the diameter of the domain, leading to stabilized methods with different stability and convergence properties.
We concentrate on two stabilized methods, namely, the classical SUPG technique and the orthogonal subscale stabilization.
We design stabilized methods based on the variational multiscale decomposition of Darcy's problem.
These stabilized methods mimic different possible functional settings of the continuous problem.
In particular, for Darcyʼs problem we are able to design stabilized methods that yield optimal convergence both for the primal and the dual problems.
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