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[CT065]

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : In this talk, we shall present a-posteriori error estimates for the fully discrete finite element approximation to the optimal control problem governed by parabolic partial differential equations where the control is acting on lower dimensional manifolds. We use piecewise linear and continuous finite elements for the approximations of state and adjoint variables whereas piecewise constant functions are employed to approximate the control variable. Moreover, the time derivative is approximated by using the backward Euler scheme. We derive a-posteriori error estimates for the various dimensions of the manifold. Numerical results reveal the effectiveness of the error estimators.
Classification : 49J20, 49K20, 65N15, 65N30
Author(s) :
- Rajen Kumar Sinha (Indian Institute of Technology Guwahati)
- Ram Manohar (Indian Institute of Technology Kanpur)

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : This talk aims to present a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $R^2$. Both the spatially discrete and the fully discrete approximations are analyzed. Due to the low regularity of the solution, the convergence analysis of such problems become challenging. A priori error bounds in the $L^2(L^2(\Omega))$-norm for both the spatially discrete and the fully discrete schemes are derived under the minimal regularity assumption the solution together with the $L^2$-projection operator and the duality argument. Numerical results are reported to support the theoretical analysis.
Classification : 49J20, 49K20, 65N15, 65N30
Author(s) :
- Jhuma Sen Gupta (BITS Pilani Hyderabad)

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : In this paper we present a numerical study of a mixed formulation of a bilateral obstacle problem based on the subdifferential $(\mu_1,\mu_2)$ of a convex function. This formulation is equivalent to a saddle point problem of which the Lagrange multipliers $(\mu_1,\mu_2)$ characterize the coincidence set of the solution with the obstacles which is one of the unknowns of the problem. We consider a discretization of the problem based on finite element method. Then, we show the convergence of the approximate solutions. Next, we propose an iterative method based on an Uzawa type algorithm to solve the discrete problem. Finally, some numerical examples are given.
Classification : 49J40, 65K15, 65N30
Author(s) :
- El Bekkaye Mermri (Faculty of Science, Mohammed Premier University, Oujda)
- Mohammed Bouchlaghem (Faculty of Science, Mohammed Premier University, Oujda )

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : I will discuss a risk-averse optimal control problem governed by an elliptic variational inequality subject to random inputs. I will derive two forms of first-order stationarity conditions for the problem by passing to the limit in a penalised and smoothed approximating control problem. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to delicate analytical challenges seemingly unique to the stochastic setting.
Classification : 49J40, 49K45, 35R60
Author(s) :
- Amal Alphonse (WIAS, Berlin)