论文标题
二阶椭圆方程的有限元近似值的均匀Hölder-norm边界
Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations
论文作者
论文摘要
我们开发了De Giorgi-Nash-Moser理论的离散对应物，该理论在连续的分段仿期仿射有限元近似二阶线性椭圆近似$ - \ nabla \ cdot（a \ nabla u）= f- \ nabla \ cdot f $ a \ a \ in \ in f $ a \ in \ cdot of cdot（a \ nabla u）上提供了统一的Hölder-norm界限。 l^\ infty（ω; \ m}^{r}^{n \ times n}）$一个均匀的椭圆形矩阵值函数，$ f \ in l^{q}（q}（ω）$，$ f \ in L^p（ω;形状的定型三角剖分，不需要是准均匀的，是一个有界的多面体Lipschitz域$ω\ subset \ mathbb {r}^n $。
We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Hölder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form $-\nabla \cdot(A\nabla u)=f-\nabla\cdot F$ with $A\in L^\infty(Ω;\mathbb{R}^{n\times n})$ a uniformly elliptic matrix-valued function, $f\in L^{q}(Ω)$, $F\in L^p(Ω;\mathbb{R}^n)$, with $p > n$ and $q > n/2$, on $A$-nonobtuse shape-regular triangulations, which are not required to be quasi-uniform, of a bounded polyhedral Lipschitz domain $Ω\subset \mathbb{R}^n$.
