The numerical discrete principle was also been used to simulate an initial geo-stress field.
From the optimality condition (25) and Example 3 we conclude that in the discrete case, unlike the continuous one, the discrete principle of the maximum (as a necessary optimality condition of first order) is strengthened at the expense of multipoint variation of control as well.
Indeed, while there is much talk today of "voice" and "authenticity" in poetry, in fact "voice --as Collected Poems revoice --asmerely an electivoice --asCollected Poems comprised of semi-discrete principles like grammar, diction, tone, syntax, parataxis, juxtaposition, ethos, logos, and pathos, and authenticity is always to be found in comerelyionan procelectiveer than produconstruction
This conclusion states that the discrete variational principles produce the discrete variational integrators, and that the multi-symplecticity of these variational integrators is presented by the discrete multi-symplectic form formula (4).
It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP).
This paper presents some new tools for enforcing discrete maximum principles and/or positivity preservation in continuous piecewise-linear finite element approximations to convection-dominated transport problems.
Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net.
This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method.
In our paper, we combine the advantages of nonstandard finite difference methods and discrete variational principles to construct multi-symplectic numerical schemes for the nonlinear Schrödinger equation with variable coefficients (1).
Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
