Sentence examples for primal variables from inspiring English sources

In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn Hilliard equation in primal variables.

Due to the spherical nature of the non-conforming interfaces the mortar method turns out to be functionally conforming and allows for an equal-order interpolation of the primal variables and the Lagrange multipliers.

The other 6 primal variables are random circles with other six colors.

DD decomposes the original problem through Lagrange decomposing method and iterates primal variables and dual variables separately[20].

As we show in the following theorem, these variables are related with the optimal primal variables (x∗,p∗).

The dual problem is simpler to solve and its solution can be used to recover primal variables (Section "Recovery of optimal primal variables") with reduced computational complexity due to the inherently separable structure of the problem Lagrangians (Section "Separability").

The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields.

Then, motivated by the numerical simulation of the primal variable and the flux in highly heterogeneous porous media, we use a multiscale mixed finite element method to solve the state equations.

We present several numerical examples and show that one needs a few test functions to achieve an error similar to the projection error in the primal variable irrespective of the Peclet number.

The problem reduces to finding a test space (a dimensionally reduced space for this auxiliary variable), which guarantees that the error in the primal variable (representing the solution) is close to the projection error of the full solution on the dimensionally reduced space that approximates the solution.

where u is the primal variable and v is the dual variable.