Space-Time Isogeometric Analysis of Parabolic Evolution Equations

TL;DR

This paper introduces a stable space-time Isogeometric Analysis method for solving parabolic evolution equations, providing theoretical error estimates and confirming results through numerical experiments.

Contribution

The paper develops a new stable space-time IgA method for parabolic equations, including theoretical analysis and validation via numerical experiments.

Findings

Elliptic bilinear form on IgA space with respect to a discrete energy norm

A priori discretization error estimates established

Numerical experiments confirm theoretical results

Abstract

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.