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An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes

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Main Author: Petr, Knobloch
Format: Book
Language:English
Published: Springer 2023
Subjects:
DMP
SMUAS
Online Access:https://link.springer.com/article/10.1007/s11075-023-01511-2
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7689
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spelling oai:localhost:PNK-76892023-04-07T09:33:01Z An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes Petr, Knobloch DMP SMUAS CC BY Algebraically stabilized finite element discretizations of scalar steady-state convection–diffusion–reaction equations often provide accurate approximate solutions satisfying the discrete maximum principle (DMP). However, it was observed that a deterioration of the accuracy and convergence rates may occur for some problems if meshes without local symmetries are used. The paper investigates these phenomena both numerically and analytically and the findings are used to design a new algebraic stabilization called Symmetrized Monotone Upwind-type Algebraically Stabilized (SMUAS) method. It is proved that the SMUAS method is linearity preserving and satisfies the DMP on arbitrary simplicial meshes. Moreover, numerical results indicate that the SMUAS method leads to optimal convergence rates on general simplicial meshes. 2023-04-07T09:33:00Z 2023-04-07T09:33:00Z 2023 Book https://link.springer.com/article/10.1007/s11075-023-01511-2 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7689 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic DMP
SMUAS
spellingShingle DMP
SMUAS
Petr, Knobloch
An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
description CC BY
format Book
author Petr, Knobloch
author_facet Petr, Knobloch
author_sort Petr, Knobloch
title An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
title_short An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
title_full An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
title_fullStr An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
title_full_unstemmed An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
title_sort algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s11075-023-01511-2
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7689
_version_ 1762546700936806400
score 8.891145

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