Iterative refinement of finite element approximations for elliptic problems
-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes
An -estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space.
-convergence of finite element Galerkin approximations for parabolic problems
-convergence of saddle-point approximations for second order problems
-error estimate for a system of elliptic quasivariational inequalities.
-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities.
-error estimates for variational inequalities with Hölder continuous obstacle
L... Stability of Finite Element Approximations to Elliptic Gradient Equations.
L2 Estimates for the Finite Element Method for the Dirichlet Problem with Singular Data.
Lagrange multipliers for higher order elliptic operators
In this paper, the Babuška’s theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions.
Lagrange multipliers for higher order elliptic operators
In this paper, the Babuška's theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions.
Legendre and Chebyshev Spectral Approximations of Burger's Equation.
Local error estimates and adaptive refinement for first-order system least squares (FOSLS).
Local error estimates for finite element discretization of the Stokes equations
Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
Maximum-Norm Stability and Error Estimates in Galerkin Methods for Parabolic Equations in One Space Variable
Mesh Refinement For Stabilized Convection Diffusion Equations
We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local
Méthodes d'éléments finis avec intégration numérique pour des problèmes elliptiques du quatrième ordre
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent norm are derived.
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.