The finite element method for elliptic problems

By Philippe G. Ciarlet. Classics in applied mathematics, 2002

10,469 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e05f82b6ba3396ddb0a69520f628ec3f29ccc9bf

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

On the Full C 1 -Q k Finite Element Spaces on Rectangles and Cuboids (2010, methodology): “We refer to Ciarlet [10] for more discussions on how to define C1 finite element spaces by high order nodal derivatives.”
A discontinuous skeletal method for the viscosity-dependent Stokes problem (2015, neutral): “The mesh sequence is assumed to be shape-regular in the sense of Ciarlet [7].”
MODIFIED MORLEY ELEMENT METHOD FOR A FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM (2006, background): “1 The Morley element and its convergence for biharmonic equations can be found in [1-3,5], while the rectangle Morley element in [7].”
Choose a Transformer: Fourier or Galerkin (2021, methodology): “Traditional methods, such as finite element/difference [20, 22], spectral methods [12], etc.”
Residual a posteriori error estimation for the Virtual Element Method for elliptic problems (2015, methodology): “The Virtual Element Method (VEM) is a very recent generalization of the Finite Element (FE) method [21,24] that achieves a higher degree of flexibility in terms of meshes and properties of the scheme by avoiding an explicit construction of the discrete shape functions.”
Reproducing kernel element method. Part I: Theoretical formulation (2004, neutral): “[4,8]), we have the error estimate ku I1;jukL2ð~ XjÞ þ hku I1;jukH1ð~ XjÞ þ h ku I1;jukL1ð~ XjÞ 6 ch 2jujH2ð~ XjÞ: ð4:8Þ”
A projection-based error analysis of HDG methods (2010, neutral): “Consider a partitioning of the domain Ω into elements K forming a mesh Th satisfying the standard finite element conditions [7]; the faces of K are going to be denoted by F .”
Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems (2016, neutral): “For arbitrary w ∈ H(Ω) and ρ ∈H(Ω), by the standard scaling argument [4], we have the following approximation properties |w − Pw|Hm(Ωh) + h1/2−m‖w − Pw‖Γh ≤ Chmin{r,k+1}−m‖w‖Hr(Ω), (A.”
Mesh Generation (2020, background): “Early results [39] showed convergence as triangular elements shrink, assuming that all angles are bounded away from 0°.”