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<p>An exponentially accurate space-time coupled nonconforming least squares spectral element method is analysed for parabolic PDEs with corner singularity emanating from the non-smoothness of the domain and space-time incompatibilities in (2+1) dimensions. A stability estimate is proved under the assumption of weighted analytic regularity of the solution and a preconditioner is defined based on the variational formulation of the scheme for the resulting discrete system, enabling the efficient implementation of the preconditioned conjugate gradient method in a matrix-free fashion and moreover, the computational complexity is derived as well. The exponential convergence of the numerical scheme along with its computational complexity are substantiated with several benchmark numerical problems via parallel programming with Message Passing Interface as the communication protocol.</p>

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Space-time Nonconforming Least Squares Spectral Element Approximation for Parabolic PDEs with Corner Singularity

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Sanuwar Ahmed Choudhury,
  • Pankaj Biswas

摘要

An exponentially accurate space-time coupled nonconforming least squares spectral element method is analysed for parabolic PDEs with corner singularity emanating from the non-smoothness of the domain and space-time incompatibilities in (2+1) dimensions. A stability estimate is proved under the assumption of weighted analytic regularity of the solution and a preconditioner is defined based on the variational formulation of the scheme for the resulting discrete system, enabling the efficient implementation of the preconditioned conjugate gradient method in a matrix-free fashion and moreover, the computational complexity is derived as well. The exponential convergence of the numerical scheme along with its computational complexity are substantiated with several benchmark numerical problems via parallel programming with Message Passing Interface as the communication protocol.