HIGH-ORDER

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New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
《Communications on Applied Mathematics and Computation》2024年第3期2011-2044,共34页Alina Chertock Michael Herty Arsen S.Iskhakov Safa Janajra Alexander Kurganov Maria Lukacova-Medvid'ova 
supported in part by the NSF grant DMS-2208438.The work of M.Herty was supported in part by the DFG(German Research Foundation)through 20021702/GRK2326,333849990/IRTG-2379,HE5386/18-1,19-2,22-1,23-1;under Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612;The work of A.Kurganov was supported in part by the NSFC grant 12171226;the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design,China(No.2019B030301001).
In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume fram...
关键词：Hyperbolic conservation and balance laws with uncertainties Finite-volume methods Central-upwind schemes Weighted essentially non-oscillatory(WENO)interpolations 
Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows
《Communications on Applied Mathematics and Computation》2024年第1期625-657,共33页Ruihan Guo Yinhua Xia 
supported by the NSFC Grant no.12271492;the Natural Science Foundation of Henan Province of China Grant no.222300420550;supported by the NSFC Grant no.12271498;the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...
关键词：Two-phase incompressible flows Fully-decoupled High-order accurate Linear implicit Spectral deferred correction method Local discontinuous Galerkin method 
High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models
《Communications on Applied Mathematics and Computation》2024年第1期372-398,共27页Wei Zheng Yan Xu 
supported by the NSFC grant 12071455.
In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...
关键词：Chemotaxis models Local discontinuous Galerkin(LDG)scheme Convex splitting method Variant energy quadratization method Scalar auxiliary variable method Spectral deferred correction method 
Preface to the Focused Issue on High-Order Numerical Methods for Evolutionary PDEs
《Communications on Applied Mathematics and Computation》2023年第2期529-531,共3页Arturo Hidalgo Michael Dumbser Eleuterio F.Toro 
The underlying fields of this special issue of CAMC include mathematical modeling through evolutionary partial differential equations(PDEs),advanced high-order non-lin-ear numerical methods for their approximation and...
关键词：HYPERBOLIC STIFF approximation 
High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation
《Communications on Applied Mathematics and Computation》2023年第1期116-142,共27页Andrew Christlieb Matthew Link Hyoseon Yang Ruimeng Chang 
AFOSR and NSF for their support of this work under grants FA9550-19-1-0281 and FA9550-17-1-0394 and NSF grant DMS 191218。
In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the targe...
关键词：Semi-Lagrangian methods WENO schemes High-order splitting methods Non-polynomial basis Vlasov equation Vlasov-Poisson system 
One-and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells
《Communications on Applied Mathematics and Computation》2023年第1期143-169,共27页M.Semplice E.Travaglia G.Puppo 
MIUR-PRIN project 2017KKJP4X“Innovative numerical methods for evolutionary partial differential equations and applications”.Gabriella Puppo acknowledges also the support of 2019 Ateneo Sapienza research project no.RM11916B51CD40E1.
We address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes,focusing in particular on the cells close to the boundaries of the domain.In fact,most techniq...
关键词：High-order finite volume schemes Boundary conditions without ghost cells Hyperbolic systems CWENOZ reconstruction Adaptive order reconstructions 
A High-Order Semi-Lagrangian Finite Difference Method for Nonlinear Vlasov and BGK Models
《Communications on Applied Mathematics and Computation》2023年第1期170-198,共29页Linjin Li Jingmei Qiu Giovanni Russo 
Research of Linjin Li and Jingmei Qiu is supported by the NSF grant NSF-DMS-1818924;the Air Force Office of Scientific Computing FA9550-18-1-0257 and the University of Delaware;the Italian Ministry of Instruction,University and Research(MIUR)to support this research with funds coming from the PRIN Project 2017,No.2017KKJP4X and ITN-ETN Horizon 2020 Project,Project Reference 642768.
In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK models.The finite difference scheme has better c...
关键词：SEMI-LAGRANGIAN WENO Finite difference Vlasov-Poisson BGK equation Linear stability 
p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with Static Condensation
《Communications on Applied Mathematics and Computation》2022年第3期783-822,共40页Lorenzo Botti Daniele A.Di Pietro 
Daniele Di Pietro acknowledges the support of Agence Nationale de la Recherche Grant fast4hho(ANR-17-CE23-0019).
We propose a p-multilevel preconditioner for hybrid high-order(HHO)discretizations of the Stokes equation,numerically assess its performance on two variants of the method,and compare with a classical discontinuous Gal...
关键词：Stokes equations Divergence free constraint Hybrid high-order Discontinuous Galerkin P-MULTIGRID Static condensation 
Preface to Focused Section on Efficient High-Order Time Discretization Methods for Partial Differential Equations
《Communications on Applied Mathematics and Computation》2021年第4期605-605,共1页Sebastiano Boscarino Giuseppe Izzo Lorenzo Pareschi Giovanni Russo Chi-Wang Shu 
During May 8-10,2019,the International Workshop on Efficient High-Order Time Discretization Methods for Partial Differential Equations took place in Villa Orlandi,Anacapri,Italy,a Congress Center of the University of ...
关键词：THANK HYPERBOLIC preserving 
High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation被引量：1
《Communications on Applied Mathematics and Computation》2020年第4期613-640,共28页Min Zhang Yang Liu Hong Li 
This work is supported by the National Natural Science Foundation of China(11661058,11761053);the Natural Science Foundation of Inner Mongolia(2017MS0107);the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07).
In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.T...
关键词：Two-dimensional nonlinear fractional difusion equation High-order LDG method Second-orderθscheme Stability and error estimate 
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