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Contents

1 [CT107]

[CT107]

Session Time & Room

CT107 (1/2) : 5B @E703 [Chair: Yohann Dudouit]
CT107 (2/2) : 5C @E703 [Chair: Amanda Emily Diegel]

Classification

CT107 (1/2) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M)
CT107 (2/2) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M)

[00798] Accelerating Low-Order Matrix-Free Finite Element Methods for Geophysics on GPU Architectures

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
Type : Contributed Talk
Abstract : Low-order matrix-free FEMs offer an alternative approach that avoids the need to construct a global stiffness matrix. In this study, we compare the performance of low-order matrix-free FEMs with a sparse-matrix approach on GPU architectures for geophysics applications. Our results show that low-order matrix-free FEMs can significantly accelerate the solution of large linear systems on GPU architectures.
Classification : 65M60, 86-08, 65F50
Format : Talk at Waseda University
Author(s) :
- Yohann Dudouit (Lawrence Livermore National Lab)
- Randy Settgast (Lawrence Livermore National Lab)
- Nicola Castelletto (Lawrence Livermore National Lab)

[00930] Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
Type : Contributed Talk
Abstract : The Ericksen--Leslie equations are used to model liquid crystals in their nematic phase. We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept satisfies the weak-strong uniqueness property. We construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm.
Classification : 65M60, 35A35, 35Q35, 76A15
Format : Talk at Waseda University
Author(s) :
- Maximilian Elias Vincenzo Reiter (Technische Universität Berlin)

[00852] Energy stable and positive DG scheme for Keller-Segel equations

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
Type : Contributed Talk
Abstract : This work is focused on discretization of the Keller-Segel equations for chemotaxis, a challenging problem due to its convective nature. Specifically, we introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin which is based on the gradient-flow structure of the equations. Also we present some numerical tests in accordance with the aforementioned properties of the discretization, showing a good behaviour in the case of chemotactic collapse, where very steep gradients appear
Classification : 65M60, 35Q92, 92-10
Format : Online Talk on Zoom
Author(s) :
- J. Rafael Rodríguez-Galván (Universidad de Cádiz)
- Francisco Guillén-González (Universidad de Sevilla)
- Daniel Acosta-Soba (Universidad de Cádiz)

[01018] VMS Stablized FEA of M-NS Equations For Nano Thermal Fluid

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
Type : Contributed Talk
Abstract : In this paper, we present a variable multiscale stabilised finite element metthod for NS equations with thermal transport for hybrid nano fluid flow. In particular algebraic approach of approximating the subscales has been considered and then the stabilization parameters are derived using Fourier analysis. Following that, we have derived an apriori error estimates. Also we have analysed the flow, velocity, pressure and temperature distribution over the bench mark problems viz. Multiply driven cavity flow.
Classification : 65M60, 65M15, 65M22
Author(s) :
- Dipak Kumar Sahoo (Indian Institute of Technology, Kanpur)
- B. V. Rathish Kumar (Indian Institute of Technology, Kanpur)
- Anil Rathi (Indian Institute of Technology, Kanpur)

[01728] C0 IP Methods for Phase Field Crystal Equations

Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
Type : Contributed Talk
Abstract : A relatively new class of mathematical models known as phase field crystal models has emerged as a way to simulate physical processes where automic- and microscales are tightly coupled. In this talk, we present numerical schemes for two such models which rely on a C0 interior penalty finite element method spatial discretization. We show that the numerical methods are unconditionally energy stable and unconditionally convergent and support our conclusions with a few numerical experiments.
Classification : 65M60, 65M12
Format : Talk at Waseda University
Author(s) :
- Amanda Emily Diegel (Mississippi State University)
- Natasha Sharma (University of Texas at El Paso)

[01105] SIPG Method for boundary control problems governed by parabolic PDEs

Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
Type : Contributed Talk
Abstract : We present a posteriori error analysis of adaptive finite element approximations for parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The discretization is followed by using the symmetric interior penalty Galerkin (SIPG) technique. Both reliable and efficient residual-based error estimators are deduced. The implementation of these error estimators serves as a guide for the adaptive mesh refinement process. The numerical experiment shows the effectiveness of the derived estimators.
Classification : 65M60, 65M15
Format : Talk at Waseda University
Author(s) :
- Ram Manohar (Indian Institute of Technology Kanpur)
- Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
- Kedarnath Buda (Indian Institute of Technology Kanpur)
- Rajen Kumar Sinha (Indian Institute of Technology Guwahati)

[02480] Conservative Timesteppers for Fluid Mechanics via Finite Elements in Time

Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
Type : Contributed Talk
Abstract : Finite-element-in-time—FET—formulations can be carefully constructed to preserve key structures in time-dependent PDEs, such as energy and helicity dissipation, material conservation, and Hamiltonians. Furthermore, with appropriate trial and test spaces, FET formulations can be solved one timestep at a time, like classical timesteppers. We propose a general auxiliary space concept that connects these ideas, using FET to derive timesteppers up to arbitrary order in time that preserve these structures. We discuss potential future applications of this idea.
Classification : 65M60, 76D05, 65P10, 76W05, 65M22
Format : Talk at Waseda University
Author(s) :
- Boris Duncan Andrews (University of Oxford)
- Patrick Emmet Farrell (University of Oxford)
- Wayne Arter (United Kingdom Atomic Energy Authority)

[00617] Low-regularity exponential-type integrators for the Zakharov system under rough data

Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
Type : Contributed Talk
Abstract : Two low-regularity exponential-type integrators (LREIs) are proposed and analyzed for the Zakharov system (ZS), including a first-order integrator and a second-order one. To my knowledge, it is the first time to propose such LREIs that achieve the first- and second-order accuracy by requiring one or two additional derivatives for the solutions of ZS, respectively. Numerical comparison with other methods demonstrates the superiority of the newly proposed LREIs for rough data.
Classification : 65M70, 65M12, 65M15, 65T50
Format : Talk at Waseda University
Author(s) :
- Hang Li (Tsinghua University )
- Chunmei Su (Tsinghua University)

[01923] Primal hybrid method for quasi-linear parabolic problems

Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
Type : Contributed Talk
Abstract : In this article, a second order quasi-linear parabolic initial-boundary value problem is approximated by using primal hybrid finite element method and Lagrange multipliers. Semi-discrete and backward Euler based fully discrete schemes are discussed and optimal order error estimates are established by applying modified elliptic projection. Optimal order error estimates in maximum norm are also derived. Earlier results on maximum-norm superconvergence of the gradient in piecewise linear finite-element approximations of elliptic and parabolic problems are now carried over to quasi-linear case using primal hybrid method. Finally, the results on numerical experiments confirm our theoretical findings.
Classification : 65M60
Author(s) :
- RAVINA SHOKEEN (The LNM Institute of Information Technology)
- Ajit Patel (The LNM Institute of Information Technology)
- Amiya Kumar Pani (BITS Goa)