On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.
On the numerical solution of some semilinear elliptic problems.
On the rate of convergence of difference schemes for the heat transfer equation on the solutions from
On the role of boundary conditions for CIP stabilization of higher order finite elements.
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...
On the stability of difference schemes for nonlinear elliptic differential equations with boundary conditions of Dirichlet type
On the tangential velocity arising in a crystalline approximation of evolving plane curves
In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.
On Two Steps Lax-Wendroff Methods in Several Dimension.
Optimal convergence of a discontinuous-Galerkin-based immersed boundary method*
We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, Int. J. Numer. Methods Eng.76 (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...
Optimal convergence of a discontinuous-Galerkin-based immersed boundary method*
We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, Int. J. Numer. Methods Eng.76 (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...
Optimal convergence rates of mortar finite element methods for second-order elliptic problems
Optimal convergence rates of hp mortar finite element methods for second-order elliptic problems
We present an improved, near-optimal hp error estimate for a non-conforming finite element method, called the mortar method (M0). We also present a new hp mortaring technique, called the mortar method (MP), and derive h, p and hp error estimates for it, in the presence of quasiuniform and non-quasiuniform meshes. Our theoretical results, augmented by the computational evidence we present, show that like (M0), (MP) is also a viable mortaring technique for the hp method.
Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Finite element semidiscrete approximations on nonlinear dynamic shallow shell models in considered. It is shown that the algorithm leads to global, optimal rates of convergence. The result presented in the paper improves upon the existing literature where the rates of convergence were derived for small initial data only [19].
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