A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation
We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For t...
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| Format: | Article |
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/22/4699 |
| _version_ | 1797458508627574784 |
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| author | Yuejie Li Zhendong Luo |
| author_facet | Yuejie Li Zhendong Luo |
| author_sort | Yuejie Li |
| collection | DOAJ |
| description | We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we first develop an FE method for the fractional Tricomi-type equation and provide the existence, unconditional stability, and error analysis for the FE solutions. We then develop the RDEFE method for the fractional Tricomi-type equation by means of the POD technique and analyze the existence, unconditional stability, and errors for the RDEFE solutions by using the matrix analysis. Lastly, we provide two numerical examples to verify our theoretical results and to explain the advantages of the RDEFE method. |
| first_indexed | 2024-03-09T16:38:07Z |
| format | Article |
| id | doaj.art-586dfe656fc54d849c70fbf56c8f8c75 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:38:07Z |
| publishDate | 2023-11-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-586dfe656fc54d849c70fbf56c8f8c752023-11-24T14:54:31ZengMDPI AGMathematics2227-73902023-11-011122469910.3390/math11224699A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type EquationYuejie Li0Zhendong Luo1Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, ChinaSchool of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaWe here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we first develop an FE method for the fractional Tricomi-type equation and provide the existence, unconditional stability, and error analysis for the FE solutions. We then develop the RDEFE method for the fractional Tricomi-type equation by means of the POD technique and analyze the existence, unconditional stability, and errors for the RDEFE solutions by using the matrix analysis. Lastly, we provide two numerical examples to verify our theoretical results and to explain the advantages of the RDEFE method.https://www.mdpi.com/2227-7390/11/22/4699proper orthogonal decompositionclassical finite element methodfractional Tricomi-type equationreduced-dimension extrapolated finite element method |
| spellingShingle | Yuejie Li Zhendong Luo A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation Mathematics proper orthogonal decomposition classical finite element method fractional Tricomi-type equation reduced-dimension extrapolated finite element method |
| title | A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation |
| title_full | A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation |
| title_fullStr | A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation |
| title_full_unstemmed | A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation |
| title_short | A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation |
| title_sort | reduced dimension extrapolating method of finite element solution coefficient vectors for fractional tricomi type equation |
| topic | proper orthogonal decomposition classical finite element method fractional Tricomi-type equation reduced-dimension extrapolated finite element method |
| url | https://www.mdpi.com/2227-7390/11/22/4699 |
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