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We show that straightforward discrete approximations to these problems yield approximate problems which are ill-posed.
Babuska & Vogelius [40] already observed for conforming discretizations, that the sequence of discrete approximations U (T ℓ ) always converges.
Additionally, it reduces, on average, the computing time of the exact methods by approximately 99%, and this offering high-quality discrete approximations of the true Pareto-front.
Then, fully discrete approximations are introduced by using the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives.
Therefore, many approximate schemes were presented, for example, EM scheme, time discrete approximations, stochastic Taylor expansions [15], and so on.
The discrete approximations have the same property.
Similar(33)
Alternatively, one could employ a discrete approximation to a continuous distribution of Arrow-Debreu prices21.
This method is based on discrete approximation of time-to-failure distributions of the system elements.
It is based on the discrete approximation of the Laplacian on an irregular grid.
The first model is an isotropic damage model and is used in the discrete approximation.
We design a non-linear time discrete approximation scheme and prove convergence of the approximations to a weak solution.
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