多面体表面上电场积分方程的自然hp边界元法的收敛性
Convergence of the Natural hp-BEM for the Electric Field Integral Equation on Polyhedral Surfaces
AI总结：
针对多面体表面上的电场积分方程，采用基于Raviart-Thomas边界元的Galerkin离散化，证明了在足够细网格或足够高多项式次数下解的渐近拟最优性。
摘要：
我们考虑有界多面体开或闭表面上的电场积分方程（EFIE）的变分形式。采用基于形状正则表面网格上局部变多项式次数的div-相容Raviart-Thomas边界元（BEM）的协调Galerkin离散化。我们建立了在足够细网格或足够高多项式次数下Galerkin解的渐近拟最优性。
英文摘要：
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on div-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degree.
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