Space-Time Isogeometric Analysis of Parabolic Evolution Problems

DI Stephen Edward Moore

Oct. 20, 2015, 3:30 p.m. S2 059

We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for
the numerical solution of parabolic evolution equations in fixed and moving spatial
computational domains. The discrete bilinear form is elliptic on the IgA space with
respect to a discrete energy norm. This property together with a corresponding
boundedness property, consistency and approximation results for the IgA spaces
yields an a priori discretization error estimate with respect to the discrete norm.
The theoretical results are confirmed by several numerical experiments with
low- and high-order IgA spaces. We also present the assembling and
solving times for the corresponding linear system of IgA equations.
Furthermore, we perform numerical experiments for space-time
problems with singularities leading to reduced convergence rate.
Mesh grading is a simple technique to recover the full rate.