ANISOTROPIC %26quot;GOAL-ORIENTED%26quot; MESH ADAPTIVITY FOR ELLIPTIC PROBLEMS

作者：Carpio Jaime^*; Luis Prieto Juan; Bermejo Rodolfo

来源：SIAM Journal on Scientific Computing, 2013, 35(2): A861-A885.

DOI：10.1137/120874606

• adaptive finite element algorithm
• unstructured triangular anisotropic meshes
• DWR method
• linear and quadratic finite elements
• patch-wise higher-order interpolation recovery

We propose in this paper an anisotropic, adaptive, finite element algorithm for steady, linear advection-diffusion-reaction problems with strong anisotropic features. The error analysis is based on the dual weighted residual methodology, allowing us to perform %26quot;goal-oriented%26quot; adaptation of a certain functional J(u) of the solution and derive an %26quot;optimal%26quot; metric tensor for local mesh adaptation with linear and quadratic finite elements. As a novelty, and to evaluate the weights of the error estimator on unstructured meshes composed of anisotropic triangles, we make use of a patchwise, higher-order interpolation recovery readily extendable to finite elements of arbitrary order. We carry out a number of numerical experiments in two dimensions so as to prove the capabilities of the goal-oriented adaptive method. We compute the convergence rate and the effectivity index for a series of output functionals of the solution. The results show the good performance of the algorithm with linear as well as quadratic finite elements.

• 出版日期2013