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We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…

Numerical Analysis · Mathematics 2025-10-08 Daozhi Han , Xiaoming Wang

An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…

Computational Physics · Physics 2024-06-17 Andrei Ludvig-Osipov , Dmytro Yadykin , Pär Strand

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…

Optimization and Control · Mathematics 2019-06-05 Brian Bullins , Richard Peng

In contrast with the diffusion equation which smoothens the initial data to $C^\infty$ for $t>0$ (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally…

Numerical Analysis · Mathematics 2023-07-17 Buyang Li , Zongze Yang , Zhi Zhou

In this paper, we introduce a fourth-order accurate finite element method for incompressible variable density flow. The method is implicit in time and constructed with the Taylor series technique, and uses standard high-order Lagrange basis…

Numerical Analysis · Mathematics 2022-09-21 Lukas Lundgren , Murtazo Nazarov

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…

Numerical Analysis · Mathematics 2018-02-26 Daniele A. Di Pietro , Stella Krell

The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…

Numerical Analysis · Mathematics 2015-05-20 Bjorn Engquist , Brittany D. Froese , Yen-Hsi Richard Tsai

In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…

Numerical Analysis · Mathematics 2022-04-06 Aikaterini Aretaki , Efthymios N. Karatzas , Georgios Katsouleas

Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…

Fluid Dynamics · Physics 2024-06-14 Hilary Weller , Christian Kuehnlein , Piotr K. Smolarkiewicz

Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making…

Fluid Dynamics · Physics 2021-10-07 Yanlin Shao , Zhiping Zheng , Hui Liang , Jikang Chen

This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…

Numerical Analysis · Mathematics 2021-10-01 Marzieh Alireza Mirhoseini , Matthew J. Zahr

We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates the need for ad hoc parameters. The viscosity is…

Numerical Analysis · Mathematics 2024-04-16 Tuan Anh Dao , Murtazo Nazarov

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical…

Optimization and Control · Mathematics 2025-10-21 Baturalp Yalcin , Jihun Kim , Javad Lavaei

This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…

Numerical Analysis · Mathematics 2026-04-22 Hao Dong

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

Numerical Analysis · Mathematics 2024-06-06 Anders Melander , Max E. Bitsch , Dong Chen , Allan P. Engsig-Karup

In a companion paper (Laibe & Price 2011b), we have presented an algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH). In this paper, we develop an implicit timestepping method that preserves the…

Instrumentation and Methods for Astrophysics · Physics 2015-06-03 Guillaume Laibe , Daniel J. Price

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features…

Numerical Analysis · Mathematics 2022-01-11 Michele Botti , Daniel Castanon Quiroz , Daniele A. Di Pietro , André Harnist

A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order…

Numerical Analysis · Mathematics 2022-06-10 Chongmin Song , Sascha Eisenträger

In this paper, for the first time a compact third-order gas-kinetic scheme is proposed on unstructured meshes for the compressible viscous flow computations. The possibility to de sign such a third-order compact scheme is due to the…

Numerical Analysis · Mathematics 2016-06-22 Liang Pan , Kun Xu

A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…

Numerical Analysis · Mathematics 2024-05-01 Sebastian Myrbäck , Sara Zahedi