共查询到4条相似文献,搜索用时 0 毫秒
1.
Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem 下载免费PDF全文
Hui Peng Qilong Zhai Ran Zhang & Shangyou Zhang 《Communications In Computational Physics》2020,28(3):1147-1175
We consider a model of coupled free and porous media flow governed by
Stokes equation and Darcy's law with the Beavers-Joseph-Saffman interface condition.
In this paper, we propose a new numerical approach for the Stokes-Darcy system. The
approach employs the classical finite element method for the Darcy region and the
weak Galerkin finite element method for the Stokes region. We construct corresponding discrete scheme and prove its well-posedness. The estimates for the corresponding numerical approximation are derived. Finally, we present some numerical experiments to validate the efficiency of the approach for solving this problem. 相似文献
2.
A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions 下载免费PDF全文
In this paper, we develop the residual based a posteriori error estimates
and the corresponding adaptive mesh refinement algorithm for atomistic/continuum
(a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is quasi-optimal if the continuum
model is discretized by P1 finite elements. The numerical results of the adaptive mesh
refinement algorithm is consistent with the quasi-optimal a priori error estimates. 相似文献
3.
A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves 下载免费PDF全文
Yingxia Xi & Xia Ji 《Communications In Computational Physics》2022,32(2):524-546
The paper presents a holomorphic operator function approach for the
transmission eigenvalue problem of elastic waves using the discontinuous Galerkin
method. To use the abstract approximation theory for holomorphic operator functions,
we rewrite the elastic transmission eigenvalue problem as the eigenvalue problem of
a holomorphic Fredholm operator function of index zero. The convergence for the
discontinuous Galerkin method is proved following the abstract theory of the holomorphic Fredholm operator. The spectral indicator method is employed to compute
the transmission eigenvalues. Extensive numerical examples are presented to validate
the theory. 相似文献
4.
A priori and a posteriori error estimates of H1‐Galerkin mixed finite element method for parabolic optimal control problems 下载免费PDF全文
In this exposition, we study both a priori and a posteriori error analysis for the H1‐Galerkin mixed finite element method for optimal control problems governed by linear parabolic equations. The state and costate variables are approximated by the lowest order Raviart‐Thomas finite element spaces, whereas the control variable is approximated by piecewise constant functions. Compared to the standard mixed finite element procedure, the present method is not subject to the Ladyzhenskaya‐Babuska‐Brezzi condition and the approximating finite element spaces are allowed to be of different degree polynomials. A priori error analysis for both the semidiscrete and the backward Euler fully discrete schemes are analyzed, and convergence properties for the state variables and the control variable are obtained. In addition, L2(L2)‐norm a posteriori error estimates for the state and control variables and ‐norm for the flux variable are also derived. 相似文献