Scholarlink

<p>We present a high-order interior penalty discontinuous Galerkin method based on a reconstructed approximation to the biharmonic equation. The first contribution is that the approximation space is reconstructed from nodal values by solving a local least squares fitting problem per element. The numerical solution converges with optimal rates under error measurements. The second contribution is that an optimal preconditioned solver is proposed to solve the linear system efficiently that not only the condition number of the preconditioned system admits a uniform upper bound independent of the mesh size, but also the solver for the preconditioning matrix is of the optimal convergence rate. Such advantages for solvers to linear systems from penalty methods are seldom attained before.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An optimal preconditioned discontinuous Galerkin method for biharmonic equation with \(C^0\)-reconstructed approximation

  • 期刊论文

  • 发表日期：

    2026年1月21日

查看全文
  • Ruo Li,
  • Qicheng Liu,
  • Fanyi Yang

摘要

We present a high-order interior penalty discontinuous Galerkin method based on a reconstructed approximation to the biharmonic equation. The first contribution is that the approximation space is reconstructed from nodal values by solving a local least squares fitting problem per element. The numerical solution converges with optimal rates under error measurements. The second contribution is that an optimal preconditioned solver is proposed to solve the linear system efficiently that not only the condition number of the preconditioned system admits a uniform upper bound independent of the mesh size, but also the solver for the preconditioning matrix is of the optimal convergence rate. Such advantages for solvers to linear systems from penalty methods are seldom attained before.