论文标题
与时间相关的反应扩散问题的平衡规范误差估计与空间变化
A balanced norm error estimation for the time-dependent reaction-diffusion problem with shift in space
论文作者
论文摘要
我们考虑了一个奇特的扰动时间依赖性问题，其空间中的移位项。在适当定义的Durán和S型网格的适当层适合网格上，我们得出了固定问题的A-Priori误差估计。使用不连续的Galerkin方法，我们获得了全部离散化的错误估计。引入加权标量产品和规范使我们能够估计能量和平衡规范中时间相关问题的错误。到目前为止，它已经开放以证明这一结果。能量规范中的误差估计是用于空间中标准有限元离散化的错误，并且对于平衡规范中的误差估计，数值解决方案的计算通过使用不同的双线性形式更改。给出一些数值结果以确认预测的理论并显示移位对解决方案的影响。
We consider a singularly perturbed time-dependent problem with a shift term in space. On appropriately defined layer adapted meshes of Durán- and S-type we derive a-priori error estimates for the stationary problem. Using a discontinuous Galerkin method in time we obtain error estimates for the full discretisation. Introduction of a weighted scalar products and norms allows us to estimate the error of the time-dependent problem in energy and balanced norm. So far it was open to prove such a result. Error estimates in the energy norm is for the standard finite element discretization in space, and for the error estimate in the balanced norm the computation of the numerical solution is changed by using a different bilinear form. Some numerical results are given to confirm the predicted theory and to show the effect of shifts on the solution.
