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11 papers found.
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An optimized finite element extrapolating method for 2D viscoelastic wave equation

In this study, we first present a classical finite element (FE) method for a two-dimensional (2D) viscoelastic wave equation and analyze the existence, stability, and convergence of the FE solutions. Then we establish an optimized FE extrapolating (OFEE) method based on a proper orthogonal decomposition (POD) method for the 2D viscoelastic wave equation and analyze the existence, ...

Stabilized finite volume element method for the 2D nonlinear incompressible viscoelastic flow equation

In this article, we devote ourselves to building a stabilized finite volume element (SFVE) method with a non-dimensional real together with two Gaussian quadratures of the nonlinear incompressible viscoelastic flow equation in a two-dimensional (2D) domain, analyzing the existence, stability, and error estimates of the SFVE solutions and verifying the validity of the preceding ...

An optimized SPDMFE extrapolation approach based on the POD technique for 2D viscoelastic wave equation

An optimized splitting positive definite mixed finite element (SPDMFE) extrapolation approach based on proper orthogonal decomposition (POD) technique is developed for the two-dimension viscoelastic wave equation (2DVWE). The errors of the optimized SPDMFE extrapolation solutions are analyzed. The implement procedure for the optimized SPDMFE extrapolation approach is offered. Some ...

A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations

In this paper, we provide a new type of study approach for the two-dimensional (2D) Sobolev equations. We first establish a semi-discrete Crank-Nicolson (CN) formulation with second-order accuracy about time for the 2D Sobolev equations. Then we directly establish a fully discrete CN finite volume element (CNFVE) formulation from the semi-discrete CN formulation about time and ...

An effective finite element Newton method for 2D p-Laplace equation with particular initial iterative function

In this article, a functional minimum problem equivalent to the p-Laplace equation is introduced, a finite element-Newton iteration formula is established, and a well-posed condition of iterative functions satisfied is provided. According to the well-posed condition, an effective initial iterative function is presented. Using the effective particular initial function and Newton ...

A high accuracy numerical method based on spectral theory of compact operator for biharmonic eigenvalue equations

In this study, a high accuracy numerical method based on the spectral theory of compact operator for biharmonic eigenvalue equations on a spherical domain is developed. By employing the orthogonal spherical polynomials approximation and the spectral theory of compact operator, the error estimates of approximate eigenvalues and eigenfunctions are provided. By adopting orthogonal ...

A highly efficient spectral-Galerkin method based on tensor product for fourth-order Steklov equation with boundary eigenvalue

Zhendong Luo 0 0 School of Mathematics and Physics, North China Electric Power University , No. 2, Bei Nong Road, Changping District, Beijing, 102206 , China 1 School of Mathematical Science, Guizhou Normal

A POD-based reduced-order TSCFE extrapolation iterative format for two-dimensional heat equations

In this article, a proper orthogonal decomposition (POD) technique is employed to establish a POD-based reduced-order time-space continuous finite element (TSCFE) extrapolation iterative format for two-dimensional (2D) heat equations, which includes very few degrees of freedom but holds sufficiently high accuracy. The error estimates of the POD-based reduced-order TSCFE solutions ...

A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations

Zhendong Luo A proper orthogonal decomposition (POD) method is used to establish a POD-based reduced-order finite difference (FD) extrapolating model with fully second-order accuracy for the non

A space-time continuous finite element method for 2D viscoelastic wave equation

In this article, we establish a space-time continuous finite element (STCFE) method for viscoelastic wave equation. The existence, uniqueness, and stability of the STCFE solutions are proved, and the optimal rates of convergence of STCFE solutions are obtained without any time and space mesh size restrictions. Two numerical examples on unstructured meshes are employed to verify the ...

A POD-based reduced-order FD extrapolating algorithm for traffic flow

A traffic flow Lighthill, Whitham, and Richards (LWR) model is studied by means of a proper orthogonal decomposition (POD) technique. A POD-based reduced-order finite difference (FD) extrapolating algorithm (FDEA) with lower dimension and fully second-order accuracy is established. Two numerical experiments are used to show that the POD reduced-order FDEA is feasible and efficient ...