Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains

Abstract

In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion problem on a moving domain is studied. For geometrically higher order accuracy, we apply a parametric mapping on a background space-time tensor-product mesh. Concerning discretisation in time, we consider discontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and Galerkin collocation methods. For stabilisation with respect to bad cut configurations and as an extension mechanism that is required for the latter two schemes, a ghost penalty stabilisation is employed. The article puts an emphasis on the techniques that allow to achieve a robust but higher order geometry handling for smooth domains. We investigate the computational properties of the respective methods in a series of numerical experiments. These include studies in different dimensions for different polynomial degrees in space and time, validating the higher order accuracy in both variables.

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Cited by in corpus (5)

• Space-time unfitted finite elements on moving explicit geometry representations
• Discretization Error Analysis of a High Order Unfitted Space-Time Method for moving domain problems
• A conservative Eulerian finite element method for transport and diffusion in moving domains
• A Higher Order Unfitted Space-Time Finite Element Method for Coupled Surface-Bulk problems
• Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods