Table 3 The \(\pmb{L^{2}}\) norm errors for functions \(\pmb{H(x,t)-\widetilde{H}(x,t)}\) and \(\pmb{u(x,t)-\widetilde{u}(x,t)}\) in Example 1
From: A Ritz-Galerkin approximation to the solution of parabolic equation with moving boundaries
( N , M ) | \(\boldsymbol {\|H(x,t)-\widetilde{H}(x,t)\|_{L^{2}([0,1]\times[0,1])}}\) | \(\boldsymbol {\|u(x,t)-\widetilde{u}(x,t)\|_{L^{2}([\varphi_{1}(t),\varphi _{2}(t)]\times[0,1])}}\) |
|---|---|---|
(2,3) | 3.34 × 10−7 | 2.74 × 10−7 |
(2,4) | 1.92 × 10−8 | 1.51 × 10−8 |
(2,5) | 2.00 × 10−10 | 1.61 × 10−10 |
(2,6) | 9.25 × 10−12 | 7.07 × 10−12 |
(2,7) | 1.06 × 10−13 | 8.30 × 10−14 |
(2,8) | 2.81 × 10−15 | 2.09 × 10−15 |