Selected Publications of Richard S. Falk
The publication information and abstract for each of the papers listed below
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desired paper. Full text versions of the paper may be viewed as PDF files.
- Local space-preserving decompositions for the bubble transform
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- Construction of polynomial preserving cochain extensions by blending
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- The Bubble Transform and the de Rham Complex
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- Hidden Positivity and a New Approach to Numerical Computation of
Hausdorff Dimension: Higher Order Methods
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- C^m Eigenfunctions of Perron-Frobenius Operators and a
New Approach to Numerical Computation of Hausdorff Dimension: Applications
in R^1
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- A New Approach to Numerical Computation of Hausdorff Dimension of
Iterated Function Systems: Applications to Complex Continued Fractions
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- C^m Eigenfunctions of Perron-Frobenius Operators and a
New Approach to Numerical Computation of Hausdorff Dimension
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- Double complexes and local cochain projections
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- The bubble transform: a new tool for
analysis of finite element methods
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- Basic principles of mixed virtual element methods
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- On the consistency of the combinatorial codifferential
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- Local bounded cochain projections
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- Stokes complexes and the construction of stable finite elements with
pointwise mass conservation
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- A mixed finite element method for EWOD that directly computes the
position of the moving interface
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- Mixed finite element approximation of the vector Laplacian with
Dirichlet boundary conditions
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- Finite element exterior calculus: from Hodge theory to
numerical stability
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- Hexahedral H(div) and H(curl) finite elements
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Geometric decompositions and local bases for spaces
of finite element differential forms
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- A Fortin operator for two-dimensional Taylor-Hood elements
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- Finite element methods for linear elasticity (corrected
version)
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- Finite elements for the Reissner-Mindlin plate
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- Finite element exterior calculus, homological techniques,
and applications
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- Locking-free Reissner-Mindlin elements without reduced
intgration
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- Mixed finite elements for linear elasticity with
weakly imposed symmetry
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- Differential complexes and stability of finite element methods.
II. The elasticity complex
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- Differential complexes and stability of finite element methods.
I. The de Rham complex
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- Quadrilateral H(div) finite elements
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- Remarks on quadrilateral Reissner-Mindlin plate elements
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- Finite element approximation on quadrilateral meshes
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- Approximation by quadrilateral finite elements
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- Analysis of finite element methods for linear hyperbolic problems
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- Similarity solutions in the theory of curvature driven diffusion along
planar curves: I. Symmetric curves expanding in time
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- Stability of cylindrical bodies in the theory of surface diffusion
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- Explicit finite element methods for linear hyperbolic systems
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- Locking-free finite elements for the Reissner-Mindlin Plate
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- Multigrid in H(div) and H(curl)
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- Analysis of a one-dimensional variational model of the equilibrium
shape of a deformable crystal
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- Explicit finite element methods for symmetric hyperbolic equations
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- Multigrid preconditioning in H(div) on non-convex polygons
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- Dimensional reduction for plates based on mixed variational
principles
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- Derivation and justification of plate models by variational methods
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- Preconditioning in H(div) and applications (conf-proc)
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- Preconditioning in H(div) and applications
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- Preconditioning discrete approximations of the Reissner-Mindlin
plate model (conf-proc)
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- Preconditioning discrete approximations of the Reissner-Mindlin
plate model
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- Space-time finite element methods for surface diffusion with
applications to the theory of stability of cylinders
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- Analysis of a linear--linear finite element for the Reissner-Mindlin
Plate Model
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- Equivalence of finite element methods for problems in
elasticity,
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- Local error estimates for a finite element method for
hyperbolic and convection-diffusion equations
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- Stability of a higher order Hood-Taylor method
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- The boundary layer for the Reissner-Mindlin plate model
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- Asymptotic analysis of the boundary layer for the Reissner-Mindlin
plate model
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- Well-posedness of the fundamental boundary value problems
for constrained anisotropic materials
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- A new mixed formulation for elasticity
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- A uniformly accurate finite element method for the
Reissner-Mindlin plate model
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- Edge effects in the Reissner-Mindlin plate theory
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- Remarks on mixed finite element methods for problems with rough coefficients
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- Convergence of a second-order scheme for the nonlinear
dynamical equations of elastic rods
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- Reduced continuity finite element methods for first order
scalar hyperbolic equations
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- Nonconforming finite element methods for the equations
of linear elasticity
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- Nonconforming finite elements for the Stokes problem
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- A finite element method for the approximation of the incompressible,
linearized Euler equations
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- Error estimates for the numerical identification of a variable
coefficient
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- Analysis of a continuous finite element scheme for hyperbolic
equations
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- Error estimates for mixed methods
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- An error estimate for the truncation method for the solution of
a parabolic variational inequality
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- A penalty and extrapolation method for
the stationary Stokes equations
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- An analysis of the penalty and extrapolation method for
the stationary Stokes equations
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- Error estimates for elasto-plastic problems
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- Error estimates for the approximation of a class of variational
inequalities
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- Approximation of a class of optimal control problems with order
of convergence estimates
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