Variational Mesh Adaptation Methods for Axisymmetrical Problems

Variational Mesh Adaptation Methods for Axisymmetrical Problems

We study variational mesh adaptation for axially symmetric solutions to twodimensional problems. The study is focused on the relationship between the mesh density distribution and the monitor function and is carried out for a traditional functional that includes several widely used variational methods as special cases and a recently proposed functional that allows for a weighting between mesh i...

A Survey of Direct Methods for Solving Variational Problems

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalen...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Variational Mesh Adaptation: Isotropyand Equidistribution

We present a new approach for developing more robust and error-oriented mesh adaptation methods. Specifically, assuming that a regular (in cell shape) and uniform (in cell size) computational mesh is used (as is commonly done in computation), we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error ...

Measuring Mesh Qualities and Application to Variational Mesh Adaptation

The mesh assessment problem is investigated in this paper by taking into account the shape and size of elements and the solution behavior. Three elementwise mesh quality measures characterizing the shape, alignment, and adaptation features of elements are introduced according to the estimates of interpolation error developed on a general mesh. An adaptive mesh is assessed by an overall quality ...