Selected Publications of Richard S. Falk

The publication information and abstract for each of the papers listed below may be seen as a plain text file by clicking on the word info next to the desired paper. Full text versions of the paper may be viewed as PDF files.

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
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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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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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Maintained by falk@math.rutgers.edu and last modified 10/23/2015.