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[CT112]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, we study a cell-centered finite volume scheme for anisotropic diffusion problems on unstructured polyhedral meshes through a certain linearity-preserving approach. The main feature of our new scheme is that the vertex unknowns are interpolated by the least square technique combined with graph search algorithm to handle arbitrary discontinuities. The search algorithm is local, and for the problem with continuous diffusion coefficients, the resulting interpolation algorithm naturally degenerates into the classical least squares algorithm. Numerical experiments show that our scheme achieves nearly second order accuracy on general unstructured grids in case that the diffusion tensor is taken to be anisotropic and heterogeneous.
Classification : 65N08, 65N06
Author(s) :
- Longshan Luo (Institute of Applied Physics and Computational Mathematics)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We formulate the oblique derivative boundary value problem applied in gravity field and present two approaches to its solution by the finite volume method. In the first approach, the oblique derivative in the boundary condition is decomposed into normal and two tangential components and approximated by the central scheme. In the second approach, the oblique derivative in the boundary condition is treated by the first order upwind scheme. Both approaches are tested by various experiments.
Classification : 65N08
Author(s) :
- Zuzana Minarechová (Slovak University of Technology)
- Marek Macák (Slovak University of Technology)
- Karol Mikula (Slovak University of Technology)
- Róbert Čunderlík (Slovak University of Technology)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin methods with residual based error estimation. In this talk we derive an adaptive refinement algorithm for an elliptic parametric PDE with unbounded lognormal diffusion coefficient steered by a reliable error estimator for both the spacial mesh and the stochastic space. Moreover, we will prove the convergence of the derived adaptive algorithm.
Classification : 65N12, 65N50, 65F10, 65F55, 65D40
Author(s) :
- Nando Farchmin (Physikalisch-Technische Bundesanstalt)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The stability analysis of numerical methods is often challenging. In this talk, compact schemes are considered for the variable coefficient PDEs arising in option pricing. A sufficient condition for stability of the schemes has been derived using novel difference equation based approach. The condition number of amplification matrix is also analyzed, and an estimate for the same is derived. An example is provided using MATLAB to support the assumption taken to assure stability.
Classification : 65N12, 65N06, 65N15
Author(s) :
- KULDIP SINGH PATEL (Indian Institute of Technology Patna)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : This talk aims at presenting a monolithic property preserving scheme solving hyperbolic PDEs on 2D unstructured grids. This method is based on both high-order discontinuous Galerkin ((DG)) and first-order Finite Volume ((FV)) schemes. Those schemes will be blended at each subcell face, in a way to impose any convex admissibility property, as for instance positivity, entropy, non-oscillatory behavior, while retaining as much as possible the very precise subcell resolution of DG schemes.
Classification : 65N12, 35L67, 65M08, 65N30
Author(s) :
- François Vilar (Montpellier University)