Space-Time Isogeometric Analysis of Parabolic Evolution Problems
DI Stephen Edward MooreOct. 20, 2015, 1:30 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.