有限體積法的期後誤差估計

Abstract

弱剩型誤差估計子被廣泛的應用在有限體積法，而且此估計子基於單元式 顯示較可取於基於體積式。因此當我們使用此誤差估計子時，有限體積法 可引用許多已證實於適應性有限單元法的重要特質﹔例如資料結構和切割 技巧。在適當的假設之下，此誤差估計子將會以間斷的Ｈ度量收斂至真正 誤差。我們並以多個數值結果驗證適應性方法使用此估計子的效率性與可 靠性。 Weak-residual type a posteriori error estimators are proposed for a fairly general class of finite volume schemes. The estim- ators are shown to be perferably based on elementwise instead of volumewise error calculations. It turns out that when using these error estimators the finite volume method can share many important features such as data structures and refinement str- ategies with the well-established finite element method in ad- aptivity. Under suitable assumptions, the error estimators are shown to converge to the exact error in the 'broken' H norm. Numerical results are given to demonstrate high quality of the estimator and the effectiveness and efficiency of the adaptive approach using this estimator.