The hp -multigrid method applied to hp -adaptive refinement of triangular grids

The hp-multigrid method applied to hp-adaptive refinement of triangular grids

Recently the hp version of the finite element method, in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials, has received increasing attention. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method, such as multigrid. An intriguing notion is to use the values o...

Strategies for hp-adaptive refinement

In the hp-adaptive version of the finite element method for solving partial differential equations, the grid is adaptively refined in both h, the size of the elements, and p, the degree of the piecewise polynomial approximation over the element. The selection of which elements to refine is determined by a local a posteriori error indicator, and is well established. But the determination of whet...

Parallel Adaptive hp - Refinement Techniques for Conservation Laws *

Abstract We describe an adaptive hp-refinement local finite element procedure for the parallel solution of hyperbolic systems of conservation laws on rectangular domains. The local finite element procedure utilizes spaces of piecewise-continuous polynomials of arbitrary degree and coordinated explicit Runge-Kutta temporal integration. A solution limiting procedure produces monotonic solutions n...

Parallelization of the multi-level hp-adaptive finite cell method

The finite cell method (FCM) introduced in [1] combines high-order finite elements with a fictitious domain approach for the solution of partial differential equations. This discretization technique yields a domain that can be easily meshed using structured grids, circumventing the tedious process of mesh generation for complex geometries. The geometry itself is resolved at integration level by...

Hp-meshless Cloud Method