Graded parametric CutFEM and CutIGA for elliptic boundary value problems in domains with corners

We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neig ...

[1]  P. Hansbo,et al.  Fictitious domain finite element methods using cut elements , 2012 .

[2]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[3]  Peter Hansbo,et al.  CutFEM: Discretizing geometry and partial differential equations , 2015 .

[4]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[5]  V. A. Kondrat'ev,et al.  Boundary problems for elliptic equations in domains with conical or angular points , 1967 .

[6]  M. Ainsworth,et al.  Aspects of an adaptive hp-finite element method : Adaptive strategy, conforming approximation and efficient solvers , 1997 .

[7]  Mats G. Larson,et al.  CutIGA with basis function removal , 2018, Adv. Model. Simul. Eng. Sci..

[8]  T. Lu,et al.  Singularities and treatments of elliptic boundary value problems , 2000 .

[9]  Vinh Phu Nguyen,et al.  Isogeometric analysis: An overview and computer implementation aspects , 2012, Math. Comput. Simul..

[10]  Harold A. Buetow,et al.  Adaptive finite element methods for differential equations , 2003, Lectures in mathematics.

[11]  M. Larson,et al.  Cut finite element methods for elliptic problems on multipatch parametric surfaces , 2017, 1703.07077.

[12]  André Massing,et al.  A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem , 2012, J. Sci. Comput..

[13]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[14]  Mats G. Larson,et al.  A new least squares stabilized Nitsche method for cut isogeometric analysis , 2018, Computer Methods in Applied Mechanics and Engineering.

[15]  Hae-Soo Oh,et al.  Mapping Techniques for Isogeometric Analysis of Elliptic Boundary Value Problems Containing Singularities , 2013 .

[16]  Hae-Soo Oh,et al.  Enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and/or corners , 2014 .

[17]  Stéphane Bordas,et al.  Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation , 2017 .

[18]  T. Belytschko,et al.  A review of extended/generalized finite element methods for material modeling , 2009 .

[19]  P. Hansbo,et al.  A FINITE ELEMENT METHOD ON COMPOSITE GRIDS BASED ON NITSCHE'S METHOD , 2003 .