论文标题
在谐波发展域上扩散方程的有限元分析
Finite element analysis for a diffusion equation on a harmonically evolving domain
论文作者
论文摘要
我们研究了不断发展的散装结构域上抛物线偏微分方程的不断发展的有限元半差异的收敛性。域的边界以给定的速度演变，然后通过求解泊松方程将其扩展到整体。抛物线方程的数值解决方案取决于大体的数值演化，该分量得出有限元方法的时间依赖性网格。稳定性分析仅适用于半差异的矩阵矢量公式，并且不需要几何参数，然后在一致性估计的证明中需要这些参数。我们提出了各种数值实验，这些实验说明了可靠的收敛速率。
We study convergence of the evolving finite element semi-discretization of a parabolic partial differential equation on an evolving bulk domain. The boundary of the domain evolves with a given velocity, which is then extended to the bulk by solving a Poisson equation. The numerical solution to the parabolic equation depends on the numerical evolution of the bulk, which yields the time-dependent mesh for the finite element method. The stability analysis works with the matrix-vector formulation of the semi-discretization only and does not require geometric arguments, which are then required in the proof of consistency estimates. We present various numerical experiments that illustrate the proven convergence rates.
