Theory and practice of finite elements

By Alexandre Ern, Jean-Luc Guermond. 2004

2,450 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/bb979ea198c152eefee1547adc29d88d67b5f682

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In Civil and Structural Engineering

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Coercive space-time finite element methods for initial boundary value problems (2020, background): “2) is a Galerkin-Petrov variational formulation, we need to establish an appropriate stability condition to ensure unique solvability; see also [14, 15, 34, 37, 43].”
An energy‐consistent material‐point method for dynamic finite deformation plasticity (2006, background): “The existence of well known pressure checkerboard modes [20], [40] precludes satisfaction of the LBB stability criterion.”
Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation (2018, background): “which is a well-posed saddle-point problem, well-approximated by the discretization (8) [15], again on the condition that the observation operator C has a unique continuation in Y.”
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems (2011, positive): “As a result, using the constant Cκ from the usual inverse inequality in the L (2)-setting [20] leads to ‖∇v‖r,T ≤ C ♯ d,k,r(T )|T | 1 r − 12 ‖∇v‖T ≤ Cκh −1 T C ♯ d,k,r(T )|T | 1 r − 12 ‖v‖T ≤ Cκh −1 T C ♯ d,k,r(T )C ♭ d,k,r(T )‖v‖r,T ≤ C ⋆ d,kCκh −1 T ‖v‖r,T , which completes the proof.”
Choose a Transformer: Fourier or Galerkin (2021, background): “The existence of an n -independent lower bound is commonly known as the discrete version of the Ladyzhenskaya–Babuška–Brezzi (LBB) condition [21, Chapter 6.12], also referred as the Banach-Neˇcas-Babuška (BNB) condition in Galerkin methods on Banach spaces [29, Theorem 2.6].”
A probabilistic model for LCF (2013, result): “In the case of a uniaxially loaded specimen, this could be a constant, while for a more complex part this can be obtained as the result of an FEA, confer [10, 11].”
Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. (2008, methodology): “Alternatively, continuous interior penalty methods [1, 6], residual free bubble methods [10, 11, 12], or subgrid modelling [8, 18] can be used for stabilizing the discretised convection-diffusion problems.”
A unified Petrov-Galerkin spectral method for fractional PDEs (2015, methodology): “2), by the Banach–Nečas–Babuška theorem [48], the error in the numerical scheme is less than or equal to a constant times the projection error.”
Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, methodology): “Finite element methods impose a richer structure on the space of weighting functions, W(W) (Ern and Guermond, 2004).”
Estimation of penalty parameters for symmetric interior penalty Galerkin methods (2007, background): “This poor coercivity property is discussed in detail in [13].”