Finite Element Methods for Elliptic Problems

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A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory (2010, background): “Therefore, the point interpolation defined here is generally different from those defined in the FEM settings where the interpolation is element based with proper mapping to ensure that the interpolant lives in a desired H1 space [31].”
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004, neutral): “[13], [15], [43]) the finite element spaces X h satisfy the standard approximation estimate, namely that for all v ∈ H(2)(D) ∩H(1) 0 (D) min χ∈Xd h ‖v − χ‖H1 0 (D) ≤ C h ‖v‖H2(D), (3.”
Design of Adaptive Finite Element Software - The Finite Element Toolbox ALBERTA (2005, background): “Starting point for the design of ALBERTA data structures is the abstract concept of a finite element space defined (similar to the definition of a single finite element by Ciarlet [25]) as a triple consisting of • a collection of mesh elements ; • a set of local basis functions on a single element, ”
An optimal control approach to a posteriori error estimation in finite element methods (2001, methodology): “Duality arguments as described above are very common in the a priori error analysis of Galerkin finite element methods (see, e.g., Ciarlet (1978) and Brenner and Scott (1994)).”