Space-Time Multi-patch Discontinuous Galerkin Isogeometric Analysis for Parabolic Evolution Problems

TL;DR

This paper introduces a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis scheme for solving parabolic evolution equations on moving domains, providing theoretical error estimates and numerical validation.

Contribution

It develops a novel stable dG-IgA method for parabolic problems on moving domains with proven error estimates and numerical experiments.

Findings

The scheme is stable and elliptic in the space-time dG norm.

Error estimates are derived for the discretization.

Numerical experiments confirm theoretical results.

Abstract

We present and analyze a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic evolution equations in moving space-time computational domains. Following \cite{LangerMooreNeumueller:2016a}, we use a time-upwind test function and apply multi-patch discontinuous Galerkin IgA methodology for discretizing the evolution problem both in space and in time. This yields a discrete bilinear form which is elliptic on the IgA space with respect to a space-time dG norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an \textit{a priori discretization} error estimate with respect to the space-time dG norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.

Figures

Full text

See pages 1-last of dGspacetime_Moore.pdf