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R Griesse and K Kunisch
P Angot F Boyer and F Hubert
F Brezzi A Buffa and K Lipnikov
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acoustic advection term algorithm applied approximation assume assumption atomistic boundary conditions bounded Cauchy-Schwarz inequality computed consider constraint continuous continuum convergence rate convex decomposition defined denote derivative differential Dirichlet boundary conditions domain EDP Sciences elliptic error estimates ESAIM existence FENE Figure finite element method finite element space flow fluid Fokker-Planck equation fracture free energy estimate Galerkin method given Hamiltonian hence holds implies inequality initial condition integral interface iteration L2-norm Lemma linear lower semicontinuity M2AN Math Mathematics Mathematics Subject Classification matrix mesh mortar finite element multilevel preconditioner Neumann boundary conditions nonlinear norm Numerical Analysis numerical schemes obtain Oldroyd-B operator optimal parameter polynomial preconditioner problem projection proof Proposition quasicontinuum rate-independent regularization Remark respectively satisfies Section smooth solitons solving stability step subdomain symmetric positive definite tensor test function Theorem triangle unique solution vector weak solution zero