Local projection methods on layer-adapted meshes for higher order discretisations of convection–diffusion problems

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• 作者：Gunar Matthies
• 关键词：Convection– ; diffusion problems ; Local projection method ; Layer-adapted mesh ; Quadrilateral finite elements
• 刊名：Applied Numerical Mathematics
• 出版年：2009
• 出版时间：October 2009
• 年：2009
• 卷：59
• 期：10
• 页码：2515-2533
• 全文大小：308 K

文摘

We consider singularly perturbed convection–diffusion problems in the unit square where the solutions show the typical exponential layers. Layer-adapted meshes (Shishkin and Bakhvalov–Shishkin meshes) and the local projection method are used to stabilise the discretised problem. Using enriched Q_r-elements on the coarse part of the mesh and standard Q_r-elements on the remaining parts of the mesh, we show that the difference between the solution of the stabilised discrete problem and a special interpolant of the solution of the continuous problem convergences ε-uniformly with order on Bakhvalov–Shishkin meshes and with order on Shishkin meshes. Furthermore, an ε-uniform convergence in the ε-weighted H¹-norm with order on Shishkin meshes and with order on Bakhvalov–Shishkin meshes will be proved. Numerical results which support the theory will be presented.