Detailed error analysis for a fractional Adams method with graded meshes

Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

Analysis of the Equilibrated Residual Method for a Posteriori Error Estimation on Meshes with Hanging Nodes

The equilibrated residual method is now accepted as the best residual type a posteriori error estimator. Nevertheless, there remains a gap in the theory and practice of the method. The present work tackles the problem of existence, construction and stability of equilibrated fluxes for hp-finite element approximation on hybrid meshes consisting of quadrilateral and triangular elements, with hang...

A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces

The Galerkin boundary element discretisations of the electric eld integral equation (EFIE) on Lipschitz polyhedral surfaces su er slow convergence rates when the underlying surface meshes are quasi-uniform and shape-regular. This is due to singular behaviour of the solution to this problem in neighbourhoods of vertices and edges of the surface. Aiming to improve convergence rates of the Galerki...

Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic var...

Pointwise a Posteriori Error Estimates for Elliptic Problems on Highly Graded Meshes

Pointwise a posteriori error estimates are derived for linear secondorder elliptic problems over general polygonal domains in 2D. The analysis carries over regardless of convexity, accounting even for slit domains, and applies to highly graded unstructured meshes as well. A key ingredient is a new asymptotic a priori estimate for regularized Green's functions. The estimators lead always to uppe...