QMR: a quasi-minimal residual method for non-Hermitian linear systems.
Quadratic finite elements with non-matching grids for the unilateral boundary contact
We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper...
Quadrature of singular integrands over surfaces.
Quantum optimal control using the adjoint method
Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal control are...
Quasi-interpolation and a posteriori error analysis in finite element methods
Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed...
Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities
Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions
Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of ℝd, d ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming...
Quasisolenoidal Velocity-Pressure Finite Element Methods for the Three-Dimensional Stokes Problem.