Name
Abstract | ||
|---|---|---|
In this paper we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-of-interest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-of-interest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to support the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/13090496X | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
adaptive mesh refinement,least-squares,finite element,error estimation | Least squares,Convergence (routing),Mathematical optimization,Finite element method,Adaptive mesh refinement,Mathematics,hp-FEM,Mixed finite element method | Journal |
Volume | Issue | ISSN |
52 | 6 | 0036-1429 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jehanzeb Hameed Chaudhry | 1 | 13 | 3.42 |
| Eric C. Cyr | 2 | 51 | 8.66 |
| Kuo Liu | 3 | 0 | 0.34 |
| Thomas A. Manteuffel | 4 | 0 | 0.34 |
| Luke Olson | 5 | 235 | 21.93 |
| Lei Tang | 6 | 0 | 0.34 |