Mortar methods with curved interfaces
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Cited by (36)
A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces
2023, Journal of Computational and Applied MathematicsCitation Excerpt :The first one comprises methods that extend classical mortars to non-coincident interfaces by treating one of the two discretized surfaces as the “true interface” over which the coupling conditions are enforced by using a projection of the state from the opposing side. We refer to [18–21] for typical examples of such methods. A second group of methods works by correcting the “energy” mismatch created by the gaps and overlaps between the discrete interfaces.
A dissimilar non-matching HDG discretization for Stokes flows
2022, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :On the other hand, unfitted methods present a more simple geometric approach, but at the cost of presenting a higher difficulty to devise high-order methods as the variational crime is much higher in this case. In the context of finite differences, the Immersed Boundary method (IB) has been shown to obtain first order accuracy for the velocity [9] and, in the case of Finite Element methods, Mortar methods have been used to impose the transmission conditions using Lagrange multipliers, but with sub-optimal convergence rates [10,11]. Higher-order results have been obtained with the Cut Finite Element method (CutFEM) [12,13], which uses a Nitsche-type approach by adding pressure stabilization and ghost penalty terms, although the results remain quasi-optimal as inf–sup stable spaces must still be chosen in this case.
An optimally convergent higher-order finite element coupling method for interface and domain decomposition problems
2020, Results in Applied MathematicsA two-scale approach for efficient on-the-fly operator assembly in massively parallel high performance multigrid codes
2017, Applied Numerical MathematicsConvergence analysis of linear or quadratic X-FEM for curved free boundaries
2014, Computer Methods in Applied Mechanics and EngineeringDistance fields on unstructured grids: Stable interpolation, assumed gradients, collision detection and gap function
2013, Computer Methods in Applied Mechanics and Engineering
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Partially supported by Deutsche Forschungsgemeinschaft, SFB 404, C12.