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[CT113]

[02694] Approximated fuzzy components scheme for convection-diffusion model

  • Session Date & Time : 5C (Aug.25, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We examine a compact technique for solving convection-diffusion models using fuzzy transform and exponential bases. The program performs approximated fuzzy components that estimate the solution values with fourth-order accuracy in an ideal computing time. The scheme uses monotone, irreducible Jacobian matrices. We will briefly discuss the new scheme's convergence theory. The usefulness of the technique will be examined by the numerical simulations of various convection-diffusion models appearing in quantum mechanics and rheological Carreau fluid.
  • Classification : 65N12, 03B80
  • Author(s) :
    • Navnit Jha (Department of Mathematics, South Asian University, Maidan Garhi, Rajpur Road, New Delhi 110 068)

[01434] Pointwise adaptive finite element method for the elliptic obstacle problem

  • Session Date & Time : 5C (Aug.25, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : In this talk, I will discuss pointwise a posteriori error analysis of a finite element method for the obstacle problem. The reliability and the efficiency of the proposed a posteriori error estimator will be discussed. In the analysis, sign property of Lagrange multipliers, Green's function estimates and the barrier functions play a crucial role. The construction of the barrier functions is based on appropriate corrections of the conforming part of the solution obtained via an enriching operator. The use of the continuous maximum principle guarantees the validity of the analysis without mesh restrictions but shape regularity. Numerical results will be presented to illustrate the performance of a posteriori error estimator.
  • Classification : 65N15, 65N30
  • Author(s) :
    • Kamana Porwal (Indian Institute of Technology Delhi, New Delhi)

[01749] Mean Field Game Partial Differential Inclusions: Analysis and Numerical Approximation

  • Session Date & Time : 5C (Aug.25, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We generalize second-order Mean Field Game PDE systems with nondifferentiable Hamiltonians to Mean Field Game Partial Differential Inclusions $($MFG PDIs$)$ by interpreting the $p$-partial derivative of the Hamiltonian in terms of subdifferentials of convex functions. We present conditions for the existence of unique weak solutions to stationary second-order MFG PDIs where the Hamiltonian is convex, Lipschitz, but possibly nondifferentiable. Moreover, we propose a strongly convergent monotone finite element scheme for the approximation of weak solutions.
  • Classification : 65N15, 65N30, PDIs in connection with mean field game theory
  • Author(s) :
    • Yohance Osborne (University College London)
    • Iain Smears (University College London)

[02236] An hp-version discontinuous Galerkin method for the generalized Burgers-Huxley Equations with weakly singular kernel

  • Session Date & Time : 5C (Aug.25, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We study the numerical approximation for the generalized Burgers-Huxley equations with a weakly singular kernel. Firstly, we derive an a priori error estimate for the hp-version of discontinuous Galerkin (DG) time stepping method. For the start-up singularities near t = 0, using geometrically refined time-steps and linearly increasing approximation orders, we get the exponential rates of convergence. For the fully discretized system we combine the DG time-stepping method and DG finite element discretization in space. Finally, the computational results are presented to validate our theoretical results.
  • Classification : 65N15, 65N30
  • Author(s) :
    • Sumit Mahajan (Indian Institute of Technology, Roorkee)
    • Arbaz Khan (IIT Roorkee)

[02462] Solving High-dimensional Inverse Problems with Weak Adversarial Networks

  • Session Date & Time : 5C (Aug.25, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We present a weak adversarial network approach to numerically solve a class of inverse problems. The weak formulation of PDE in the inverse problem is leveraged with DNNs and induces a minimax problem. Then, the solution can be solved by finding the saddle points in the network parameters. As the parameters are updated, the network gradually approximates the solution of the inverse problem. Numerical experiments demonstrate the promising accuracy and efficiency of this approach.
  • Classification : 65N21
  • Author(s) :
    • yaohua zang
    • Yaohua Zang (Zhejiang University)
    • Gang Bao (Zhejiang University)
    • Xiaojing Ye (Georgia State University)
    • Haomin Zhou (Georgia Institute of Technology)