Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform numerical method. These schemes satisfy a discrete maximum principle. In the classical case, the numerical approximations converge, in the maximum pointwise norm, at a rate of second order and the approximations converge at a rate of first order for all values of the singular perturbation parameter.

翻译：针对二维空间中的奇异摄动对流扩散问题，构造了拟合有限元方法。采用指数样条作为基函数，结合Shishkin网格，得到了稳定的参数一致数值方法。这些格式满足离散最大值原理。在经典情形下，数值近似在最大逐点范数下以二阶收敛；对于所有奇异摄动参数值，近似解均保持一阶收敛率。