Symplectic-mixed finite element approximation of linear acoustic wave equations
Symplectic-mixed finite element approximation of linear acoustic wave equations
复制标题
线性声波方程的辛混合有限元近似
作者：
R. Kirby;T. Kieu
We apply mixed finite element approximations to the first-order form of the acoustic wave equation. The semidiscrete method exactly conserves the system energy. A fully discrete method employing the symplectic Euler time method in time exactly conserves a positive-definite pertubed energy functional that is equivalent to the actual energy under a CFL condition. In addition to proving optimal-order L∞(L2)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^infty (L^2)$$end{document} estimates, we also develop a bootstrap technique that allows us to derive stability and error bounds for the time derivatives and divergence of the vector variable beyond the standard under some additional regularity assumptions.
We apply mixed finite element approximations to the first-order form of the acoustic wave equation. The semidiscrete method exactly conserves the system energy. A fully discrete method employing the symplectic Euler time method in time exactly conserves a positive-definite pertubed energy functional that is equivalent to the actual energy under a CFL condition. In addition to proving optimal-order L∞(L2)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^infty (L^2)$$end{document} estimates, we also develop a bootstrap technique that allows us to derive stability and error bounds for the time derivatives and divergence of the vector variable beyond the standard under some additional regularity assumptions.