arXiv subjects

Chenguang Zhou

Publications and source records attributed to Chenguang Zhou.

9 recordsLinked to original sources

arXiv2026

Mini mixed finite element method for nearly incompressible linear elasticity problems

This paper addresses the numerical solution of nearly incompressible linear elasticity boundary value problems and their associated eigenvalue problems. A mixed finite element formulation based on Mini element is proposed to circumvent the locking phenomenon that plagues standard low-order elements in the nearly incompressible limit. For the boundary value problem, we establish the well-posedness of mixed variational formulation and derive a priori error estimates that are uniform with respect to the Lam\'{e} constant $\underline{\lambda}$, thereby proving the method's locking-free property. For the eigenvalue problem, we develop an efficient non-nested augmented subspace algorithm designed within the mixed finite element framework. A comprehensive convergence analysis is provided for the discrete eigenvalue approximation and the proposed iterative solver, demonstrating that the convergence rates remain independent of $\underline{\lambda}$. Numerical experiments on both problems confirm the theoretical conclusions, showing optimal convergence rates and robustness as $\underline{\lambda} \to \infty$. The results validate the effectiveness of Mini element and proposed augmented subspace algorithm for reliable and efficient computation in the nearly incompressible regime.

math.NA↗

arXiv2026

Optimal error estimates of sequential finite element method for nonlinear thermo-poroelasticity problems

This study introduces and analyzes a three-step sequential decoupling algorithm designed to address nonlinear, fully coupled quasi-static thermo-poroelasticity systems incorporating convective transport. The finite element method is employed for spatial discretization and the backward Euler method for temporal discretization. The proposed sequential method has a higher computing efficiency than the fully implicit nonlinear numerical scheme, since it does not require any internal iterations. The well-posedness of the numerical solution is discussed by introducing a cut-off operator and the stability analysis of the algorithm is performed. Rigorous analysis yields optimal convergence order estimates for both spatial and temporal discretizations. In order to confirm the theoretical results and the effectiveness of the suggested approach, numerical experiments are finally carried out.

math.NA↗

arXiv2025

Sequential symmetric interior penalty discontinuous Galerkin method for fully coupled quasi-static thermo-poroelasticity problems

In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin method is employed for spatial discretization and the backward Euler method for temporal discretization. Unlike other splitting algorithms, this type of sequential method does not require any internal iterations and the computational efficiency is higher than that of the fully implicit nonlinear numerical scheme. In the theoretical analysis, a cut-off operator is introduced to prove the existence and uniqueness of numerical solution and the stability analysis of numerical scheme is conducted. Then, we derive the optimal convergence order estimates in space and time. Finally, several numerical examples are presented to illustrate the accuracy and efficiency of our proposed method.

math.NA↗

arXiv2025

A machine learning model for skillful climate system prediction

Climate system models (CSMs), through integrating cross-sphere interactions among the atmosphere, ocean, land, and cryosphere, have emerged as pivotal tools for deciphering climate dynamics and improving forecasting capabilities. Recent breakthroughs in artificial intelligence (AI)-driven meteorological modeling have demonstrated remarkable success in single-sphere systems and partially spheres coupled systems. However, the development of a fully coupled AI-based climate system model encompassing atmosphere-ocean-land-sea ice interactions has remained an unresolved challenge. This paper introduces FengShun-CSM, an AI-based CSM model that provides 60-day global daily forecasts for 29 critical variables across atmospheric, oceanic, terrestrial, and cryospheric domains. The model significantly outperforms the European Centre for Medium-Range Weather Forecasts (ECMWF) subseasonal-to-seasonal (S2S) model in predicting most variables, particularly precipitation, land surface, and oceanic components. This enhanced capability is primarily attributed to its improved representation of intra-seasonal variability modes, most notably the Madden-Julian Oscillation (MJO). Remarkably, FengShun-CSM exhibits substantial potential in predicting subseasonal extreme events. Such breakthroughs will advance its applications in meteorological disaster mitigation, marine ecosystem conservation, and agricultural productivity enhancement. Furthermore, it validates the feasibility of developing AI-powered CSMs through machine learning technologies, establishing a transformative paradigm for next-generation Earth system modeling.

cs.LG↗

arXiv2024

Enhanced Error Estimates for Augmented Subspace Method with Crouzeix-Raviart Element

In this paper, we present some enhanced error estimates for augmented subspace methods with the nonconforming Crouzeix-Raviart (CR) element. Before the novel estimates, we derive the explicit error estimates for the case of single eigenpair and multiple eigenpairs based on our defined spectral projection operators, respectively. Then we first strictly prove that the CR element based augmented subspace method exhibits the second-order convergence rate between the two steps of the augmented subspace iteration, which coincides with the practical experimental results. The algebraic error estimates of second order for the augmented subspace method explicitly elucidate the dependence of the convergence rate of the algebraic error on the coarse space, which provides new insights into the performance of the augmented subspace method. Numerical experiments are finally supplied to verify these new estimate results and the efficiency of our algorithms.

math.NA↗

arXiv2024

Augmented Subspace Scheme for Eigenvalue Problem by Weak Galerkin Finite Element Method

This study proposes a class of augmented subspace schemes for the weak Galerkin (WG) finite element method used to solve eigenvalue problems. The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigenfunction approximations in the WG finite element space defined on the fine mesh. Based on this augmented subspace, solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented subspace. The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size, as demonstrated by the accompanying error estimates. Finally, a few numerical examples are provided to validate the proposed numerical techniques.

math.NA↗

arXiv2022

Weak Galerkin finite element method for linear poroelasticity problems

This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and discrete time WG schemes, and obtain their optimal convergence order estimates in a discrete $H^1$ norm for the displacement and in an $H^1$ type and $L^2$ norms for the pressure. Finally, numerical experiments are presented to illustrate the theoretical error results in different kinds of meshes which shows the WG flexibility for mesh selections, and to verify the locking-free property of our proposed method.

math.NA↗

arXiv2021

Enhanced Error Estimates for Augmented Subspace Method

In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subspace methods have the second order convergence rate which is better than the existing results. These sharper estimates provide a new dependence of convergence rate on the coarse spaces in augmented subspace methods. These new results are also validated by some numerical examples.

math.NA↗

arXiv2020

A Nonnested Augmented Subspace Method for Eigenvalue Problems with Curved Interfaces

In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving eigenvalue problems with curved interfaces. The augmented subspace algorithm and the corresponding multilevel correction method are designed based on a coarse finite element space which is not the subset of the finer finite element space. The nonnested augmented subspace method can transform the eigenvalue problem solving on the finest mesh to the solving linear equation on the same mesh and small scale eigenvalue problem on the low dimensional augmented subspace. The corresponding theoretical analysis and numerical experiments are provided to demonstrate the efficiency of the proposed algorithms.

math.NA↗