Next Article in Journal
Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
Previous Article in Journal
Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination
Open AccessArticle

The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
Mathematics 2020, 8(8), 1261; https://doi.org/10.3390/math8081261
Received: 13 July 2020 / Revised: 24 July 2020 / Accepted: 31 July 2020 / Published: 1 August 2020
(This article belongs to the Section Computational Mathematics)
This study is mainly concerned with the reduced-order extrapolating technique about the unknown solution coefficient vectors in the Crank-Nicolson finite element (CNFE) method for the parabolic type partial differential equation (PDE). For this purpose, the CNFE method and the existence, stability, and error estimates about the CNFE solutions for the parabolic type PDE are first derived. Next, a reduced-order extrapolating CNFE (ROECNFE) model in matrix-form is established with a proper orthogonal decomposition (POD) method, and the existence, stability, and error estimates of the ROECNFE solutions are proved by matrix theory, resulting in an graceful theoretical development. Specially, our study exposes that the ROECNFE method has the same basis functions and the same accuracy as the CNFE method. Lastly, some numeric tests are shown to computationally verify the validity and correctness about the ROECNFE method. View Full-Text
Keywords: reduced-order extrapolating Crank-Nicolson finite element method; parabolic type partial differential equation; existence and stability as well as error estimates reduced-order extrapolating Crank-Nicolson finite element method; parabolic type partial differential equation; existence and stability as well as error estimates
Show Figures

Figure 1

  • Externally hosted supplementary file 1
    Doi: mathematics-880486
MDPI and ACS Style

Luo, Z. The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation. Mathematics 2020, 8, 1261.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop