We extend the phi-FD finite-difference scheme, which handles domains described by a level-set function on a Cartesian grid, to Neumann boundary conditions. The condition is relaxed near the boundary through the level-set and an auxiliary field, which is eliminated by writing the relaxed condition at a boundary node and at its nearest interior node. The scheme uses only interior nodes and the level-set: no ghost values, flux reconstruction or cut-cell volumes. We prove optimal consistency and show second-order convergence in the L2, H1 and Linf norms on a non-convex domain. Two elementary precautions, an individual normalization of the boundary equations and a rule for the choice of the coupled interior node, make the condition number O(h^-2) and independent of the smallest cut cell, without any stabilization term.
We give a one-sided stability argument for high-order cut finite elements with symmetric Nitsche boundary conditions. On each boundary patch, an $H^1$-projection splits the discrete function into a single polynomial and a stabilized residual. Inward segments control the polynomial inside the physical domain; complete-e...
Erik Burman, P. Hansbo, M. G. Larson et al.· 0 citations
In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the {\phi}-FEM paradigm in which the computational domain is described implicitly by a level-set function {\phi}. This function is incorporated into the variational formulation in order...
Michel Duprez, Johan Marguet, Alexei Lozinski et al.· 0 citations
In this paper, we present a family of high-order cut finite element methods based on the discontinuous Galerkin (DG) framework for scalar hyperbolic conservation laws on complex domains. Building on our previous work, we develop a multidimensional formulation that combines macro-element stabilization with flux limiting...
We introduce and analyze a two-level overlapping additive Schwarz preconditioner for discontinuous Galerkin discretizations of virtual element spaces on general polygonal meshes in two dimensions, for a second-order elliptic problem whose coefficient is constant on each subdomain and may have large jumps across the int...
A ghost-point immersed boundary method is coupled with auxiliary differential equations to impose a locally-reacting impedance condition on a wall that does not conform to a Cartesian grid, in the framework of the linearized Euler equations. The ghost-point reconstruction follows the normal-stencil approach: an ellipti...
Abdoulaye Ouattara· 0 citations
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