Symmetrized Two-Scale Finite Element Discretizations for Partial Differential Equations with Symmetric Solutions
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Pengyu Hou
und
Aihui Zhou
Abstract
In this paper, some symmetrized two-scale finite element methods are proposed for a class of partial differential equations with symmetric solutions.
With these methods, the finite element approximation on a fine tensor-product grid is reduced to the finite element approximations on a much coarser grid and a univariant fine grid.
It is shown by both theory and numerics including electronic structure calculations that the resulting approximations still maintain an asymptotically optimal accuracy.
By symmetrized two-scale finite element methods, the computational cost can be reduced further by a factor of 𝑑 approximately compared with two-scale finite element methods when
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11971066
Award Identifier / Grant number: 11771467
Funding source: National Key Research and Development Program of China
Award Identifier / Grant number: 2019YFA0709600
Award Identifier / Grant number: 2019YFA0709601
Funding statement: P. Hou was partially supported by the National Natural Science Foundation of China (grant 11971066). F. Liu was partially supported by the National Natural Science Foundation of China (grant 11771467) and the disciplinary funding of Central University of Finance and Economics. A. Zhou was partially supported by the National Key R & D Program of China under grants 2019YFA0709600 and 2019YFA0709601.
Acknowledgements
The authors thank Professor Huajie Chen for enlightening discussions and the referees for their helpful comments and suggestions.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
- Numerical Approximation of Gaussian Random Fields on Closed Surfaces
- Multivariate Analysis-Suitable T-Splines of Arbitrary Degree
- Symmetrized Two-Scale Finite Element Discretizations for Partial Differential Equations with Symmetric Solutions
- Relaxation Quadratic Approximation Greedy Pursuit Method Based on Sparse Learning
- Optimal Pressure Recovery Using an Ultra-Weak Finite Element Method for the Pressure Poisson Equation and a Least-Squares Approach for the Gradient Equation
- Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations
- An Optimal Method for High-Order Mixed Derivatives of Bivariate Functions
- A Convenient Inclusion of Inhomogeneous Boundary Conditions in Minimal Residual Methods
- A 𝐶1-𝑃7 Bell Finite Element on Triangle
- A Conforming Virtual Element Method for Parabolic Integro-Differential Equations
- Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes
Artikel in diesem Heft
- Frontmatter
- Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
- Numerical Approximation of Gaussian Random Fields on Closed Surfaces
- Multivariate Analysis-Suitable T-Splines of Arbitrary Degree
- Symmetrized Two-Scale Finite Element Discretizations for Partial Differential Equations with Symmetric Solutions
- Relaxation Quadratic Approximation Greedy Pursuit Method Based on Sparse Learning
- Optimal Pressure Recovery Using an Ultra-Weak Finite Element Method for the Pressure Poisson Equation and a Least-Squares Approach for the Gradient Equation
- Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations
- An Optimal Method for High-Order Mixed Derivatives of Bivariate Functions
- A Convenient Inclusion of Inhomogeneous Boundary Conditions in Minimal Residual Methods
- A 𝐶1-𝑃7 Bell Finite Element on Triangle
- A Conforming Virtual Element Method for Parabolic Integro-Differential Equations
- Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes
