We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with a stability result we have estimates for the subsequent numerical analysis. With classical layer adapted meshes we present a numerical method, that achieves supercloseness and optimal convergence orders in the associated energy norm. We also consider coarser meshes in view of the weak layers. Some numerical examples conclude the paper and support the theory.

翻译：我们考虑一类带有移位项的一维四阶奇异摄动问题。通过将解展开为光滑项、边界层及内层项，得到形式解分解，并结合稳定性结果，为后续数值分析提供了估计。采用经典层适应网格，我们提出了一种数值方法，该方法在相关能量范数下可实现超收敛性和最优收敛阶。同时针对弱层考虑了更稀疏的网格。最后通过数值算例验证了理论分析结果。