A Cut Discontinuous Galerkin Method for Coupled Bulk-Surface Problems

We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured, unfitted background mesh. By adding certain stabilization terms to the discrete variational formulation of the coupled bulk-surface problem, the resulting cutDGM is provably stable and exhibits optimal convergence properties as demon- strated by numerical experiments. We also show both theoretically and numerically that the system matrix is well-conditioned, irrespective of the relative position of the bulk domain in the background mesh.Comment: 22 pages, 4 figures, 1 tabl

A stabilized cut discontinuous Galerkin framework: I. Elliptic boundary value and interface problems

We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of el- liptic boundary value and interface problems on complicated domains. The domain of interest is embedded in a structured, unfitted background mesh in R d , so that the boundary or interface can cut through it in an arbitrary fashion. The method is based on an unfitted variant of the classical symmetric interior penalty method using piecewise discontinuous polynomials defined on the back- ground mesh. Instead of the cell agglomeration technique commonly used in previously introduced unfitted discontinuous Galerkin methods, we employ and extend ghost penalty techniques from recently developed continuous cut finite element methods, which allows for a minimal extension of existing fitted discontinuous Galerkin software to handle unfitted geometries. Identifying four abstract assumptions on the ghost penalty, we derive geometrically robust a priori error and con- dition number estimates for the Poisson boundary value problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. We also demonstrate how the framework can be elegantly applied to discretize high contrast interface problems. The theoretical results are illustrated by a number of numerical experiments for various approximation orders and for two and three-dimensional test problems.Comment: 35 pages, 12 figures, 2 table

Safeguarding intangible cultural heritage in an ethnic theme park setting – the case of Binglanggu in Hainan Province, China

Since 2003, safeguarding intangible cultural heritage has become a priority of China’s cultural heritage safeguarding policies at all levels. Despite this, academic research has paid limited attention to the safeguarding of ICH in a theme park setting. This paper examines the opportunities and challenges of safeguarding ICH in an ethnic theme park in China. It investigates how the Binglanggu theme park in Hainan aims to contribute to the safeguarding of Li minority heritage. The study is based on qualitative data consisting of interviews with Li minority members working at Binglanggu, the Vice-Manager of the theme park and interviews with heritage and tourism experts in Hainan, as well as observation at the theme park. The findings indicate that, when concentrating on certain ICH expressions that align with the state’s ethnic minority narrative, the theme park makes an important contribution to the research and documentation of Li minority heritage. However, the park struggles to transmit ICH expressions to the younger generations. The research concludes that essential criteria to contribute to the safeguarding of ICH are to include the ethnic minority group in the safeguarding process, for example by employing them in management positions, and to concentrate more strongly on education and transmission

A note on the penalty parameter in Nitsche's method for unfitted boundary value problems

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. From the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors