ngsxfem is an add-on library to Netgen/NGSolve, a general purpose, high performance finite element for the numerical solution of partial differential equations.The enables use geometrically unfitted technologies known under different labels, e.g.XFEM, CutFEM, TraceFEM, Finite Cell, fictitious domain method or Cut-Cell methods, etc.. Both, Netgen/NGSolve and are written in C++ with rich Python interface through which it typically used.ngsxfem academic software.Its primary intention facilitate...

Abstract In Heimann, Lehrenfeld, and Preuß (2023, SIAM J. Sci. Comp., 45(2), B139–B165), new geometrically unfitted space–time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space time have been introduced. For a parametric mapping background tensor-product mesh has used. this paper, we concentrate the geometrical approximation derive rigorous bounds distance between realized an ideal different norms results regularity mapping....

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 domain is studied. For accuracy, apply parametric mapping background tensor-product mesh. Concerning discretisation time, consider discontinuous Galerkin, as well related continuous (Petrov-)Galerkin Galerkin collocation methods. stabilisation with...

In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and time have been introduced. For a parametric mapping background tensor-product mesh has used. this paper, we concentrate the geometrical approximation derive rigorous bounds distance between realized an ideal different norms results regularity mapping. These...

We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput. 45(2), 2023, B139 - B165) the bulk case with Sass, Reusken (Comput. Math. Appl. 146(15), 253-270) surface case. The geometry is allowed to change time, discrete approximation of this ensured time-dependent isoparametric mapping. discretisation approach allows...

We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. methods allow for reduction in the number of degrees freedom Galerkin methods, thereby, costs solving arising linear systems significantly. This work shows that they are also an excellent way to reduce setting. present unified analysis class with different stabilisation mechanisms deal small cuts between geometry and mesh. cover stability derive a-priori error bounds, including errors...

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 domain is studied. For accuracy, apply parametric mapping background tensor-product mesh. Concerning discretisation time, consider discontinuous Galerkin, as well related continuous (Petrov-)Galerkin Galerkin collocation methods. stabilisation with...

We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. methods allow for reduction in the number of degrees freedom Galerkin methods, thereby, costs solving arising linear systems significantly. This work shows that they are also an excellent way to reduce setting. present unified analysis class with different stabilisation mechanisms deal small cuts between geometry and mesh. cover stability derive a-priori error bounds, including errors...