An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10)

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isogeometric analysis on multipatch surfaces, A contact algorithm for voxel-based meshes using an implicit boundary representation, Analysis of the shifted boundary method for the Stokes problem, A two-grid method for semi-linear elliptic interface problems by partially penalized immersed finite element methods, The shifted boundary method for embedded domain computations. I: Poisson and Stokes problems, The shifted boundary method for embedded domain computations. II: Linear advection-diffusion and incompressible Navier-Stokes equations, A conforming enriched finite element method for Stokes interface problems, A note on the stability parameter in Nitsche's method for unfitted boundary value problems, A residual-driven local iterative corrector scheme for the multiscale finite element method, Error estimates in weighted Sobolev norms for finite element immersed interface methods, An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions, Convergence of a linearized second-order BDF-FEM for nonlinear parabolic interface problems, A new unfitted stabilized Nitsche's finite element method for Stokes interface problems, Weak Dirichlet boundary conditions for trimmed thin isogeometric shells, A NURBS-based finite cell method for structural topology optimization under geometric constraints, A finite element method for Allen-Cahn equation on deforming surface, Variationally derived interface stabilization for discrete multiphase flows and relation with the ghost-penalty method, The second-generation shifted boundary method and its numerical analysis, Multimesh finite elements with flexible mesh sizes, A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean, A multimesh finite element method for the Navier-Stokes equations based on projection methods, Element boundary terms in reduced order models for flow problems: domain decomposition and adaptive coarse mesh hyper-reduction, Nitsche's method for linear Kirchhoff-Love shells: formulation, error analysis, and verification, The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications, A sharp interface method using enriched finite elements for elliptic interface problems, An optimal multigrid algorithm for the combining $P_1$-$Q_1$ finite element approximations of interface problems based on local anisotropic fitting meshes, Comparison of shape derivatives using CutFEM for ill-posed Bernoulli free boundary problem, Unfitted Nitsche's method for computing wave modes in topological materials, A family of two-grid partially penalized immersed finite element methods for semi-linear parabolic interface problems, High-order finite element methods for interface problems: theory and implementations, Linking ghost penalty and aggregated unfitted methods, A cut finite-element method for fracture and contact problems in large-deformation solid mechanics, An adaptive high-order unfitted finite element method for elliptic interface problems, High order interface-penalty finite element methods for elliptic interface problems with Robin jump conditions, An interface penalty parameter free nonconforming cut finite element method for elliptic interface problems, Corrected finite element methods on unfitted meshes for Stokes moving interface problem, A Nitsche mixed extended finite element method for the biharmonic interface problem, Anisotropic adaptive body-fitted meshes for CFD, A new primal-dual weak Galerkin method for elliptic interface problems with low regularity assumptions, A posteriori error estimation and adaptive mesh refinement for parabolic interface problems using non-conforming immersed finite element method, A weak Galerkin method for elasticity interface problems, Octree-based integration scheme with merged sub-cells for the finite cell method: application to non-linear problems in 3D, Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer, An unfitted finite element method by direct extension for elliptic problems on domains with curved boundaries and interfaces, An over-penalized weak Galerkin method for parabolic interface problems with time-dependent coefficients, Robust high-order unfitted finite elements by interpolation-based discrete extension, Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

Cites Work