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1 [CT104]

[CT104]

[00945] NUMERICAL ANALYSIS OF A NONLINEAR DISCRETE DUALITY FINITE VOLUME SCHEME FOR LERAY-LIONS TYPE ELLIPTIC PROBLEMS IN ORLICZ SPACES

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : In this work, we develop a finite volume approximation for general nonlinear Leray-Lions problems in the Orlicz-Sobolev framework. We prove the existence and uniqueness and some a priori estimate of the approximate solution. We establish a discrete version of Poincar\'{e} inequality and a result of discrete compactness which allows us to prove the convergence towards the weak solution of the continuous problem. Some numerical tests are provided on general meshes.
Classification : 65M12, 65M08, 76S05
Author(s) :
- Mohamed RHOUDAF ( University Moulay Ismail- Meknes)

[00962] Discontinuous Galerkin method for a high order nonlocal conservation law

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : We consider a Direct Discontinuous Galerkin (DDG) method for solving a time dependent partial differential equation with convection-diffusion terms and a fractional operator of order $\alpha \in (1,2)$. This equation was introduced to describe dunes morphodynamics and was then used for signal processing. For the DDG method, suitable numerical fluxes are introduced. We prove nonlinear stability estimates along with convergence results. Numerical experiments are given to illustrate behaviors of solutions and to verify convergence order.
Classification : 65M12, 65M60, 26A33
Author(s) :
- Afaf Bouharguane (Université de Bordeaux/INRIA)
- Afaf Bouharguane (University of Bordeaux)
- Nour Seloula (University of Caen)

[00983] Effective time step analysis of numerical schemes for gradient flows

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : A gradient flow has an important role in PDEs and it has a variety of applications including biological fields. In this talk, we briefly introduce the unconditionally stable numerical schemes for type of gradient flows and analyze them by comparing the real and its rescaled time steps, which has been a critical issue in this field. Some numerical simulations are performed to confirm our result.
Classification : 65M12
Author(s) :
- Seunggyu Lee (Korea University)
- Woon-Jae Hwang (Korea University)

[01006] VMS-based Stabilized FE Analysis of Time-dependent Coupled Unified Stokes-Brinkman-Transport Model

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : We present a Variational Multi-Scale (VMS)-based stabilized FE analysis for completely unified unsteady Stokes-Brinkman model with standard continuity and Beavers-Joseph-Saffman interface conditions, strongly coupled with transient transport equation. The fluids’ viscosities depend on the solute concentration. A simplified algebraic subgrid multiscale approach with time-dependent sub-scales is employed. A fully-implicit Euler scheme is used for time-discretization. We analyse the stability and convergence properties of the method. Appropriate numerical experiments are conducted to verify the method’s credibility.
Classification : 65M12, 65M22, 65M60
Author(s) :
- Manisha Chowdhury (Indian Institute of Technology Jodhpur)
- B.V. Rathish Kumar (Indian Institute of Technology Kanpur)

[01365] Non symmetric discontinuous Galerkin method for fractional differential equations

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : We study discontinuous Galerkin method for non-autonomous TF-ADR initial boundary value problems (IBVPs) with time fractional derivative of Caputo type. Recently, many efforts have been made to develop effective numerical methods for solving time-fractional problems. One of the typical direct numerical methods is the L1-Scheme, which can be viewed as a piecewise linear approximation to the fractional derivative. We used the classical L1-schemes for time discretization and discontinuous Galerkin method for space variable. Error bounds are established in the discrete energy norm. Finally, the convergence result is verified numerically.
Classification : 65M12, 65M15, 65M60
Author(s) :
- GAUTAM SINGH (NIT TIRUCHIRAPPALLI)

[01986] Low regularity time integration of NLS via discrete Bourgain spaces

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We study a filtered Lie splitting scheme for the cubic periodic nonlinear Schrödinger equation on the torus $\mathbb{T}^d$ with $d\geq1$. This scheme overcomes the standard stability restriction $s>\frac d2$ in Sobolev spaces $H^s(\mathbb{T}^d)$ and now allows us to handle initial data in $H^s$ for $s>0$ when $d=1,2$ and $s>\frac d2-1$ when $d\geq3$. Moreover, we establish low regularity error estimates in discrete Bourgain spaces, and prove convergence of order $\tau^{\frac s2}$ in $L^2(\mathbb{T}^d)$, where $\tau$ denotes the time step size.
Classification : 65M12, 65M15, 35Q55
Author(s) :
- Lun Ji (Universität Innsbruck)
- Alexander Ostermann (Universität Innsbruck)
- Frédéric Rousset (Université Paris-Saclay)
- Katharina Schratz (Sorbonne Université)

[02248] Remedies for entropy growth from iterative methods in CFD

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We explore the influence of iterative methods on entropy-conserving and dissipative discretizations of nonlinear conservation laws with implicit time discretizations. Newton's method can cause entropy dissipative schemes to become anti-dissipative, even with smaller iteration errors than time integration errors. We suggest various remedies and find a relaxation technique to be the most effective. Numerical experiments with dispersive wave equations demonstrate that entropy conservation produces more accurate results than non-conservative schemes, even with larger tolerances.
Classification : 65M12, 65N22, 65H10, 65F10
Author(s) :
- Viktor Linders (Lund University)
- Philipp Birken (Lund University)

[02568] A pressure-stabilized projection Lagrange--Galerkin scheme for the transient Oseen problem

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We propose and analyze a pressure-stabilized projection Lagrange--Galerkin scheme for the transient Oseen problem. The proposed scheme inherits the advantages from the projection Lagrange--Galerkin scheme: computational efficiency and essential unconditional stability. Here we also use the equal-order approximation for the velocity and pressure, and add a symmetric pressure stabilization term. This enriched pressure space enables us to obtain accurate solutions for small viscosity.
Classification : 65M12, 65M25, 65M60, 76D07, 76M10
Author(s) :
- Shinya Uchiumi (Gakushuin University)

[02608] Explorative computing for stable and consistent kinetic relaxation in lattice Boltzmann methods

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : Using lattice Boltzmann methods with multiple relaxation times for robust and fast incompressible turbulent flow simulations requires tuning of the kinetic parameters. We outsource the perfect parallelizability of lattice Boltzmann methods to analyze kinetic relaxation with respect to non-linear stability and consistency based on explorative computing of artificial turbulence in three dimensions. Conclusively, numerical indication is provided, that accuracy and dissipation is adaptively balanced near the Bhatnagar–Gross–Krook single relaxation time approximated in the scale-resolving limit.
Classification : 65M12, 35Q20, 35Q30, 76D05
Author(s) :
- Stephan Simonis (Karlsruhe Institute of Technology)
- Mathias J. Krause (Karlsruhe Institute of Technology)

[02337] Numerical analysis for the cancer invasion system with nonlocal diffusion

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : Cancer modelling is challenging in grounds of capturing the physics behind it and performing numerical simulations. In this work, we analyze the cancer invasion model with nonlocal diffusion. First, the Galerkin finite element scheme is implemented to the given system of equations for spatial discretization. Then, backward Euler scheme is applied for temporal discretization. Further, a priori error bounds and convergence estimates for the fully-discrete problem are derived. Numerical tests provided validate the theoretical studies.
Classification : 65M15, 65M60, 92B05
Author(s) :
- Kausika Chellamuthu (Bharathiar University, Coimbatore 641046, Tamil Nadu.)
- Manimaran Jeyaraj (Vellore Institute of Technology)
- Manimaran Jeyaraj (Vellore Institute of Technology, Chennai Campus, Chennai - 600127.)