ON THE SOLVABILITY OF THE NONLINEAR PROBLEMS IN AN ALGEBRAICALLY STABILIZED FINITE ELEMENT METHOD FOR EVOLUTIONARY TRANSPORT-DOMINATED EQUATIONS

被引：5
作者：
John, Volker [1 ,2 ]
Knobloch, Petr [3 ]
Korsmeier, Paul [2 ]
机构：
[1] Leibniz Inst Forsch Verbund Berlin eV WIAS, Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany
[2] Free Univ Berlin, Dept Math & Comp Sci, Arnimallee 6, D-14195 Berlin, Germany
[3] Charles Univ Prague, Dept Numer Math, Fac Math & Phys, Sokolovska 83, Prague 18675 8, Czech Republic
来源：
MATHEMATICS OF COMPUTATION | 2021年 / 90卷 / 328期
关键词：
FLUX-CORRECTION; MAXIMUM-PRINCIPLE; FEM-FCT; DIFFUSION; APPROXIMATIONS; ALGORITHMS; SCHEMES;
D O I：
10.1090/mcom/3576
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The so-called FEM-FCT (finite element method flux-corrected transport) scheme for evolutionary scalar convection-dominated equations leads in each time instant to a nonlinear problem. For sufficiently small time steps, the existence and uniqueness of a solution of these problems is shown. Moreover, the convergence of a semi-smooth Newton's method is studied.
引用
收藏
页码：595 / 611
页数：17
相关论文
共 26 条
[1]   Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization [J].
Badia, Santiago ;
Bonilla, Jesus .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 313 :133-158
[2]   ON MONOTONICITY-PRESERVING STABILIZED FINITE ELEMENT APPROXIMATIONS OF TRANSPORT PROBLEMS [J].
Badia, Santiago ;
Hierro, Alba .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2014, 36 (06) :A2673-A2697
[3]   An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes [J].
Barrenechea, Gabriel R. ;
John, Volker ;
Knobloch, Petr .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2017, 27 (03) :525-548
[4]   Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes [J].
Barrenechea, Gabriel R. ;
Burman, Erik ;
Karakatsani, Fotini .
NUMERISCHE MATHEMATIK, 2017, 135 (02) :521-545
[5]   ANALYSIS OF ALGEBRAIC FLUX CORRECTION SCHEMES [J].
Barrenechea, Gabriel R. ;
John, Volker ;
Knobloch, Petr .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (04) :2427-2451
[6]   Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension [J].
Barrenechea, Gabriel R. ;
John, Volker ;
Knobloch, Petr .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2015, 35 (04) :1729-1756
[7]  
Barrenechea Gabriel R., 2018, SeMA Journal, V75, P655
[8]   FLUX-CORRECTED TRANSPORT .1. SHASTA, A FLUID TRANSPORT ALGORITHM THAT WORKS [J].
BORIS, JP ;
BOOK, DL .
JOURNAL OF COMPUTATIONAL PHYSICS, 1973, 11 (01) :38-69
[9]   A monotonicity preserving, nonlinear, finite element upwind method for the transport equation [J].
Burman, Erik .
APPLIED MATHEMATICS LETTERS, 2015, 49 :141-146
[10]  
CLARKE F. H., 1983, Can. Math. Soc. Ser. Monogr. Adv. Texts
123