Sparse space‐time Galerkin BEM for the nonstationary heat equation
Sparse space‐time Galerkin BEM for the nonstationary heat equation
复制标题
非平稳热方程的稀疏时空伽辽金边界元法
DOI：
10.1002/zamm.201100192
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Christoph Schwab
中科院分区：
文献类型：
--
作者：
Alexey Chernov;Christoph Schwab
我们构造并分析了非定常扩散方程在Dirichlet或Neumann边界条件下边界降阶所产生的边界积分方程的稀疏张化时空Galerkin离散格式。该方法基于双正交多级子空间分解和加权稀疏张量积构造。我们将该方法的收敛行为与标准的全张量积离散方法进行了比较。特别地，对于有界二维或三维空间区域中的非定常热传导问题，我们证明了低阶稀疏时空Galerkin格式在对解的正则性要求较低的情况下，在能量范数的Galerkin误差的渐近收敛速度方面与高阶全张量积离散格式是竞争的。
We construct and analyze sparse tensorized space‐time Galerkin discretizations for boundary integral equations resulting from the boundary reduction of nonstationary diffusion equations with either Dirichlet or Neumann boundary conditions. The approach is based on biorthogonal multilevel subspace decompositions and a weighted sparse tensor product construction. We compare the convergence behavior of the proposed method to the standard full tensor product discretizations. In particular, we show for the problem of nonstationary heat conduction in a bounded two‐ or three‐dimensional spatial domain that low order sparse space‐time Galerkin schemes are competitive with high order full tensor product discretizations in terms of the asymptotic convergence rate of the Galerkin error in the energy norms, under lower regularity requirements on the solution.