Resumo: Several physical and engineering systems in the real world can be modeled using partial differential equations (PDEs). In such scenarios, one requires the input data like information about the domain, forcing term, initial/boundary conditions, etc. It is presumed that the input data is determined exactly. However, it might not always be the case. In numerical modeling, some degree of uncertainty is inevitable in the input data that would be useful in describing some physics of interest in the model. Thus, there is a need to study mathematical models that include uncertainty, resulting in PDEs with random input data. In this talk, we discuss a posteriori error estimates of parabolic PDEs with small random input data that appears in a wide range of applications. To this end, we apply the perturbation technique to deal with uncertainty. In view of this technique, solving a PDE with small random input data is equivalent to solving the decoupled deterministic problems. The approximated solutions for these problems can be obtained using the standard finite element method for the physical space approximation and different time-stepping schemes for time discretization.

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