论文标题
与不兼容边界/初始数据的奇异扰动对流 - 扩散抛物线问题
A singularly perturbed convection-diffusion parabolic problem with incompatible boundary/initial data
论文作者
论文摘要
检查了具有不兼容的流入边界和初始条件的对流扩散类型的奇异扰动抛物线问题。在恒定系数的情况下，确定了一组单数函数，它们与数据中的某些不兼容匹配，并且还满足相关的同质微分方程。当对流系数仅取决于时间变量并且初始/边界数据不连续时，则采用混合的分析/数值方法。在可变系数和满足兼容性的零级别（即连续边界/初始数据）的情况下，构建了一种数值方法，其收敛顺序被证明取决于数据满足的下一个兼容性。提出了数值结果，以支持本文中研究的两种方法建立的理论误差界限。
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain incompatibilities in the data and also satisfy the associated homogenous differential equation. When the convective coefficient only depends on the time variable and the initial/boundary data is discontinuous, then a mixed analytical/numerical approach is taken. In the case of variable coefficients and the zero level of compatibility being satisfied (i.e. continuous boundary/initial data), a numerical method is constructed whose order of convergence is shown to depend on the next level of compatibility being satisfied by the data. Numerical results are presented to support the theoretical error bounds established for both of the approaches examined in the paper.
