Sobolev方程的弱有限元方法
|
摘要
本文针对混合格式的Sobolev方程提出了一种新的弱有限元方法,建立了对应的半离散格式。该格式引入了弱散度算子及边界稳定性。经证明此半离散格式存在唯一的稳定解及最优误差估计。
In this paper, a new weak Galerkin finite element method for Sobolev equations of mixed formulation is proposed,and the corresponding semi-discrete scheme is established. The weak divergence operator and boundary stability are introduced into the scheme. It is proved that the semi-discrete scheme has unique stable solution and optimal error estimate.
In this paper, a new weak Galerkin finite element method for Sobolev equations of mixed formulation is proposed,and the corresponding semi-discrete scheme is established. The weak divergence operator and boundary stability are introduced into the scheme. It is proved that the semi-discrete scheme has unique stable solution and optimal error estimate.
引文
[1] Cockburn B, Shu C W. TVB Runge-Kutta local projection discontinuous Glerkin finite element method for conservation laws II:general framework[J]. Math. Comp., 1989,52:411-435.
[2] Arnold D N, Brezzi F, Cockburn B, Marini D. Unified analysis of discontinuous Galerkin methods for elliptic problem[J]. SIAM J.Numer. Anal.,2002,39:1749-1779.
[3] Cockburn B, Kanschat G, Schotzau D, Schwab C. Local discontinuous Galerkin methods for the Stokes system[J].SIAM J.Numer. Anal.,2002,40:319-343.
[4] Wang J and Wang C. Weak Galerkin finite element methods for elliptic PDEs(in Chinese)[J]. Sci. Sin. Math.,2015,45:1061-1092.
[5]Wang J and Ye X. A Weak Galerkinfinite element method for the Stokes equations[J].Advance in Comp. Math.,2016,42:155-174.
[6] Chen G, Feng M and Xie X. Robust globally divergence-free weak Galerkin methods for Stokes equations[J]. J.Comp. Math.,2016,34:549-572.
[7]GaoF,and Wang X. A modified weak Galerkin finite element method for Sobolevequation[J]. J. Comput. Math.,2015,33:307-322.
[8] Gao F, Cui J and Zhao G. Weak Galerkin finite element methods for Sobolevequation[J]. J. Comp. Appli. Math.,2017,317:188-202.
[2] Arnold D N, Brezzi F, Cockburn B, Marini D. Unified analysis of discontinuous Galerkin methods for elliptic problem[J]. SIAM J.Numer. Anal.,2002,39:1749-1779.
[3] Cockburn B, Kanschat G, Schotzau D, Schwab C. Local discontinuous Galerkin methods for the Stokes system[J].SIAM J.Numer. Anal.,2002,40:319-343.
[4] Wang J and Wang C. Weak Galerkin finite element methods for elliptic PDEs(in Chinese)[J]. Sci. Sin. Math.,2015,45:1061-1092.
[5]Wang J and Ye X. A Weak Galerkinfinite element method for the Stokes equations[J].Advance in Comp. Math.,2016,42:155-174.
[6] Chen G, Feng M and Xie X. Robust globally divergence-free weak Galerkin methods for Stokes equations[J]. J.Comp. Math.,2016,34:549-572.
[7]GaoF,and Wang X. A modified weak Galerkin finite element method for Sobolevequation[J]. J. Comput. Math.,2015,33:307-322.
[8] Gao F, Cui J and Zhao G. Weak Galerkin finite element methods for Sobolevequation[J]. J. Comp. Appli. Math.,2017,317:188-202.