Quasi-uniform and unconditional superconvergence analysis of Ciarlet–Raviart scheme for the fourth order singularly perturbed Bi-wave problem modeling d-wave superconductors
作者：
Highlights：
• Two implicit Backward Euler and Crank-Nicolson formulas of Ciarlet–Raviart MFEMs are presented for the time-dependent Bi-wave problem modeling d-wave superconductors by the bilinear element. The well-posedness of the weak solution and the approximation solutions are proved through Faedo-Galerkin technique and Brouwer fixed point theorem, respectively. The quasi-uniform and unconditional superconvergent estimates of O(h2+τ) and O(h2+τ2) in the broken H1-norm are obtained independent of the negative powers of the perturbation parameter. Some numerical results are provided to illustrate the theoretical analysis.
• Bi-wave problem.
• Ciarlet-Raviart method.
• Well-posedness.
• Quasi-uniform and unconditional superconvergence.
摘要
•Two implicit Backward Euler and Crank-Nicolson formulas of Ciarlet–Raviart MFEMs are presented for the time-dependent Bi-wave problem modeling d-wave superconductors by the bilinear element. The well-posedness of the weak solution and the approximation solutions are proved through Faedo-Galerkin technique and Brouwer fixed point theorem, respectively. The quasi-uniform and unconditional superconvergent estimates of O(h2+τ) and O(h2+τ2) in the broken H1-norm are obtained independent of the negative powers of the perturbation parameter. Some numerical results are provided to illustrate the theoretical analysis.•Bi-wave problem.•Ciarlet-Raviart method.•Well-posedness.•Quasi-uniform and unconditional superconvergence.
论文关键词：Bi-wave problem,Ciarlet–Raviart method,Well-posedness,Quasi-uniform and unconditional Superconvergence
论文评审过程：Received 27 June 2020, Revised 10 December 2020, Accepted 19 December 2020, Available online 11 January 2021, Version of Record 11 January 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125924
