A greedy MLPG method for identifying a control parameter in 2D parabolic PDEs

In this paper, we consider coefficient inverse problems, which are associated with the identification of unknown time dependent control parameter and unknown solution of two-dimensional parabolic inverse problem with overspecialization at a point in the spatial domain. After suitable finite difference approximation of time variable, an MLPG method is used for spatial discretization. To improve the efficiency of the MLPG method, a greedy algorithm is used. In fact, using the greedy algorithm, we avoid using more points from the data site than absolutely necessary and therefore, the method becomes more efficient. Comparison of the different kind of point selection and the effect of noisy data are performed for four test problems while our last test problem considers a problem with unknown solution. The results reveal that the method is efficient.