# Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations > 26 > 2 > 290 - 304

*x*

_{h}, we get a higher accuracy approximation

*I*${\text{\hspace{0.17em}}}_{\text{2}\text{h}}^{\text{2}\text{r}\text{\u20101}}$

*x*

_{h}, whose convergence order is the same as that of the iterated collocation method. Such an interpolation postprocessing method is much simpler. Also,...

Numerical Methods for Partial Differential Equations > 27 > 5 > 1253 - 1261

*W*

^{1,1}‐seminorm of the discrete derivative Green's function is given. Finally, we prove that the derivatives of the finite...

Numerical Methods for Partial Differential Equations > 28 > 1 > 115 - 126

*inf‐sup*condition. Then, we derive general superconvergence results for this stabilized method by using a local coarse mesh

*L*

^{2}projection. These supervergence results have three prominent...

Numerical Methods for Partial Differential Equations > 28 > 3 > 966 - 983

Numerical Methods for Partial Differential Equations > 28 > 4 > 1382 - 1398

*O*(

*h*${\text{\hspace{0.17em}}}_{\text{p}}^{\text{r}\text{+2}}$) with respect to the parameter

*h*

_{p}, which is one order higher than the conventional Galerkin or mixed...

Numerical Methods for Partial Differential Equations > 28 > 6 > 1794 - 1816

*L*

^{2}norm are proved for several semidiscrete and fully discrete schemes developed for solving this model using nonuniform cubic and rectangular edge elements. Furthermore,

*L*

^{∞}superconvergence at element centers is proved for the lowest order...

Numerical Methods for Partial Differential Equations > 29 > 1 > 280 - 296

Numerical Methods for Partial Differential Equations > 29 > 3 > 1043 - 1055

*W*

^{1,1}‐seminorm of the discrete derivative Green's function is also given. Finally, we show that the derivatives of the finite...

Numerical Methods for Partial Differential Equations > 29 > 6 > 1801 - 1820

Numerical Methods for Partial Differential Equations > 30 > 1 > 175 - 186

Numerical Methods for Partial Differential Equations > 30 > 1 > 222 - 238

Numerical Methods for Partial Differential Equations > 30 > 2 > 550 - 566

^{1}finite element method of degree

*p*on a modified Shishkin mesh. In particular, a superconvergence error bound of ${({N}^{-1}\mathrm{ln}(N+1\left)\right)}^{p}$ in a discrete energy norm is established. The error bound is uniformly valid with respect to the singular...

Numerical Methods for Partial Differential Equations > 30 > 3 > 862 - 901

*pth*‐degree polynomial spaces...

Numerical Methods for Partial Differential Equations > 30 > 4 > 1152 - 1168

*H*

^{1}‐superconvergence result: $\left|\right|{\Pi}_{h}u-{u}_{h}|{|}_{1}=O({h}^{2})$. Then, we present a gradient recovery formula and prove that the recovery gradient possesses...

Numerical Methods for Partial Differential Equations > 30 > 5 > 1633 - 1653

Numerical Methods for Partial Differential Equations > 31 > 4 > 1190 - 1208

Numerical Methods for Partial Differential Equations > 31 > 5 > 1534 - 1550

Numerical Methods for Partial Differential Equations > 31 > 5 > 1461 - 1491

*L*

^{2}error estimates...

Numerical Methods for Partial Differential Equations > 32 > 2 > 646 - 660

*Q*

_{1}(CNR

*Q*

_{1}) element, and the pressure is approximated by the piecewise constant functions. Under some regularity assumptions, the superconvergence estimates for both the velocity in broken...

Numerical Methods for Partial Differential Equations > 32 > 6 > 1647 - 1666