Multimesh finite elements with flexible mesh sizes

Convergence of finite elements enriched with mesh-less methods

Finite Elements with mesh refinement for wave equations in polygons

Error estimates for the space-semidiscrete approximation of solutions of the wave equation in polygons G ⊂ R are presented. Based on corner asymptotics of solutions of the wave equation, it is shown that for continuous, simplicial Lagrangian Finite Elements of polynomial degree p ≥ 1 with either suitably graded mesh refinement or with bisection tree mesh refinement towards the corners of G, the...

Mesh-Centered Finite Differences from Nodal Finite Elements

After it is shown that the classical ve points mesh-centered nite diierence scheme can be derived from a low order nodal nite element scheme by using nonstandard quadrature formulae, higher order block mesh-centered nite diierence schemes for second-order elliptic problems are derived from higher order nodal nite elements with nonstandard quadrature formulae as before, combined to a procedure k...

Adaptive Multilevel Finite Elements for Mesh Optimization and Visualization

Multilevel representations and mesh reduction techniques have been used for accelerating the processing and the rendering of large datasets representing scalar or vector valued functions defined on complex 2 or 3 dimensional meshes. We present a method based on finite elements and hierarchical bases which combines these two approaches in a new and unique way that is conceptually simple and theo...

The Finite Element Method With Nonuniform Mesh Sizes for Unbounded Domains

The finite element method with nonuniform mesh sizes is employed to approximately solve elliptic boundary value problems in unbounded domains. Consider the following model problem: -Am ■ / in Qc, u = g on 3ß, -~+ u = ol ] as r — |jc| -» oo, where ßc is the complement in R 3 (three-dimensional Euclidean space) of a bounded set il with smooth boundary 3Í2, / and g are smooth functions, and / has ...