A Finite Element Method for the Tricomi Problem.
A finite element method on composite grids based on Nitsche’s method
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
A finite element method on composite grids based on Nitsche's method
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation
Skeletal patterning in the vertebrate limb, i.e., the spatiotemporal regulation of cartilage differentiation (chondrogenesis) during embryogenesis and regeneration, is one of the best studied examples of a multicellular developmental process. Recently [Alber et al., The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, Bulletin of Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation reaction-diffusion system was developed to describe the interaction...
A Finite Element Procedure of the Second Order of Accuracy.
A finite element solution for plasticity with strain-hardening
A finite element solution of the monlinear heat equation
A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
We present a finite volume method based on the integration of the Laplace equation on both the cells of a primal almost arbitrary two-dimensional mesh and those of a dual mesh obtained by joining the centers of the cells of the primal mesh. The key ingredient is the definition of discrete gradient and divergence operators verifying a discrete Green formula. This method generalizes an existing finite volume method that requires “Voronoi-type” meshes. We show the equivalence of this finite volume...
A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
We present a finite volume method based on the integration of the Laplace equation on both the cells of a primal almost arbitrary two-dimensional mesh and those of a dual mesh obtained by joining the centers of the cells of the primal mesh. The key ingredient is the definition of discrete gradient and divergence operators verifying a discrete Green formula. This method generalizes an existing finite volume method that requires “Voronoi-type” meshes. We show the equivalence of this finite volume...
A Finite-Difference Approximation for the Eigenvalue of the Clamped Plate.
A first order accuracy scheme on non-uniform mesh.
A fixed point formulation of the -means algorithm and a connection to Mumford-Shah.
A fixed point method to compute solvents of matrix polynomials
Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.
A Floating-Point Technique for Extending the Available Precision.
A footnote on quaternion block-tridiagonal systems.
A forced quasilinear wave equation with dissipation
A Fortin operator for two-dimensional Taylor-Hood elements
A standard method for proving the inf-sup condition implying stability of finite element approximations for the stationary Stokes equations is to construct a Fortin operator. In this paper, we show how this can be done for two-dimensional triangular and rectangular Taylor-Hood methods, which use continuous piecewise polynomial approximations for both velocity and pressure.
A Fourier approach to model electromagnetic fields scattered by a buried rectangular cavity.
A frequency decomposition waveform relaxation algorithm for semilinear evolution equations.
A frictionless contact problem for viscoelastic materials.