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The new approach is compared to the classical discontinuous simple shear model of ECAE.
In the classical Discontinuous Deformation Analysis (DDA) the contact conditions are enforced by what is referred to as open close iteration.
A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity.
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Recently, a new unified convergence analysis for (C^{1} -conforming FEs, classical nonconforming FEs, and discontinuous FEMs for problem (1} -conforminged in [17, 18].
Compared to the classical Galerkin method, the discontinuous Galerkin method is very well suited for adaptive control of error and can deliver high orders of accuracy when the exact solution is sufficiently smooth.
Then u is an entropy solution of equation (1.1). in any piecewise continuous domain, u satisfies (1.1) in the classical sense; along any discontinuous line (x=x t)) the following Rankine-Hugoniot condition holds: bigl ubigl(x^,tbigr -ubigl(x^,tbigr -ubiglfrac{dx^,tbigr bigrubigl(x^,tbigr)bigr)-frac{dxbigl(x^,tbigr) bigr); (2.5).
The discontinuous behavior hinders classical gradient-based or response surface-based optimization.
By analyzing the discontinuous phenomenon of classical disturbance compensation techniques, this study presents a simple approach to construct a continuous compensator satisfying the finite-time disturbance rejection performance.
Unlike classical CDI, which is a discontinuous or semi-continuous process due to the need for regeneration of the electrodes within the same module, flow-electrodes offer new design opportunities which enable fully continuous desalination processes as well as easily scalable systems.
In the classical case, i.e., without discontinuous points, Dauge and Helffer in [25] found that the Neumann eigenvalues are differentiable functions of the right endpoint b satisfying a differential equation of the form lambda '=u^{2} q-lambda w).
The parabolic approximation is applied to smoothing the discontinuous deformation obtained by the classical ray theory.
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