The a posteriori estimation of the error is obtained by solving an advection reaction equation for the error, which is approximated with quadratic interpolation functions.
All of the results are compared to the optimal solution which is approximated by solving a trajectory optimization problem with a sufficiently large time horizon.
Corn seed are used as a model material and their shape is captured using X-Ray Tomography (XRT), which is approximated in the DEM by clumped spheres.
The effects of the control singularity and unknown input saturation are combined with the external disturbance which is approximated using the disturbance observer.
The acoustic pressure is described by a hybrid layer potential, the density of which is approximated by a linear combination of orthogonal polynomials.
Using the convex model theory, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one.
Within an individual region, an empirical probability distribution function based on annual snow load maxima at the observation stations is created, the upper tail of which is approximated by probability distribution functions of heavy and light tails.
It is based on the application of the Lifshitz Slyozov Wagner procedure of Ostwald ripening theory to a self-similar particle volume evolution equation which is approximated by a quadratic polynomial of the scaled particle size.
The new spectral-projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a singular boundary condition which is approximated to within a desired accuracy by using a smooth boundary condition.
The copper texture is obtained in the center layer that is plane strain compressed while the shear texture in the surface layer, which is approximated by major {001}〈011〉 and minor {111}〈112〉 and {111}〈110〉 components.
The CM is described locally by a general Probability Density Function (PDF), which is approximated by a truncated spectral expansion with a number of 'components' much smaller than the number of chemical components in the original mixture.
