Corrigendum to: A variational $\boldsymbol{H}({\rm div})$ finite-element discretization approach for perfect incompressible fluids
Andrea Natale, Colin J. Cotter · IMA Journal of Numerical Analysis · 2017
The authors of the above paper wish to inform readers that the following corrections were made post-publication: |${\sf A}^h\in {{\mathfrak{g}}}_h(V_h)$| on page 16 was corrected to: |${\sf A}^h\in S_h(V_h)$| on page 21 |${\frac{{\mathrm{d}}}{{\mathrm{d}} t}}\bigg|_{t=0}\langle u, \widehat{(g^h_t)^{-1} {\sf X}^h_{\bf c} g_t^h} \rangle = 0,$| was corrected to: |${\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0}\langle u, \widehat{g^h_t{\sf X}^h_{\bf c} (g_t^h)^{-1}} \rangle = 0,$| |$[{\sf X}^h_{\bf u},{\sf X}^h_{\bf c}]={\mathrm{ad}}_{{\sf X}^h_{\bf u}}{\sf X}^h_{\bf c} = -{\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0} {\frac{{\mathrm{d}}}{{\mathrm{d}} s}}\bigg|_{s=0} (g_t^h)^{-1} q_s^h g_t^h = {\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0} (g^h_t)^{-1} {\sf X}^h_{\bf c} g_t^h.$| was corrected to: |$[{\sf X}^h_{\bf u},{\sf X}^h_{\bf c}]={\mathrm{ad}}_{{\sf X}^h_{\bf u}}{\sf X}^h_{\bf c} = {\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0} {\frac{{\mathrm{d}}}{{\mathrm{d}} s}}\bigg|_{s=0} g_t^h q_s^h (g_t^h)^{-1} = -{\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0} g^h_t {\sf X}^h_{\bf c} (g_t^h)^{-1}.$| and |${\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0} \langle u, \widehat{(g^h_t)^{-1} {\sf X}^h_{\bf c} g_t^h} \rangle = \langle \dot{u}, {\bf c} \rangle|_{t=0} + \langle {u}, [\widehat{{\sf X}^h_{\bf u},{\sf X}^h_{\bf c}}] \rangle|_{t=0} = 0.$| was corrected to: |${\frac{{\mathrm{d}} }{{\mathrm{d}} t}}\bigg|_{t=0} \langle u, \widehat{g^h_t{\sf X}^h_{\bf c} (g_t^h)^{-1}} \rangle = \langle \dot{u}, {\bf c} \rangle|_{t=0} -\langle {u}, [\widehat{{\sf X}^h_{\bf u},{\sf X}^h_{\bf c}}] \rangle|_{t=0} = 0.$| The authors apologize for the errors.