Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping

作者：

Highlights：

• The linearized backward Euler scheme is presented for the transient Stokes equations with damping.

• The lowest-order Bernadi-Raugel rectangular element pair is used to approximate the velocity and pressure, and unconditional optimal error estimates are derived on structured rectangular meshes.

• Unconditional superclose and superconvergent results are obtained for the velocity in the norm L∞(H1) and pressure in the norm L∞(L2) on structured rectangular meshes.

摘要

•The linearized backward Euler scheme is presented for the transient Stokes equations with damping.•The lowest-order Bernadi-Raugel rectangular element pair is used to approximate the velocity and pressure, and unconditional optimal error estimates are derived on structured rectangular meshes.•Unconditional superclose and superconvergent results are obtained for the velocity in the norm L∞(H1) and pressure in the norm L∞(L2) on structured rectangular meshes.

论文关键词：Stokes equations with damping,Linearized backward Euler scheme,Unconditional optimal error estimates,Superclose and superconvergent results

论文评审过程：Received 9 February 2020, Revised 22 July 2020, Accepted 26 July 2020, Available online 11 August 2020, Version of Record 11 August 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125572