A two-grid characteristic finite volume element method for semilinear advection-dominated diffusion equations

作者：Chen, Chuanjun^*; Liu, Wei; Bi, Chunjia

来源：Numerical Methods for Partial Differential Equations, 2013, 29(5): 1543-1562.

DOI：10.1002/num.21766

• advection-dominated diffusion equations
• error estimate
• finite volume element method
• modified method of characteristics
• two grid

A two-grid finite volume element method, combined with the modified method of characteristics, is presented and analyzed for semilinear time-dependent advection-dominated diffusion equations in two space dimensions. h) is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse-grid space (with grid size H) and a linear system on the fine-grid space. An optimal error estimate in H-1 -norm is obtained for the two-grid method. It shows that the two-grid method achieves asymptotically optimal approximation, as long as the mesh sizes satisfy h = O(H-2). Numerical example is presented to validate the usefulness and efficiency of the method.

• 出版日期2013-9
• 单位山东财经大学; 烟台大学