Conservative and accurate solution transfer between high-order and low-order refined finite element spaces

by   Tzanio Kolev, et al.

In this paper we introduce general transfer operators between high-order and low-order refined finite element spaces that can be used to couple high-order and low-order simulations. Under natural restrictions on the low-order refined space we prove that both the high-to-low-order and low-to-high-order linear mappings are conservative, constant preserving and high-order accurate. While the proofs apply to affine geometries, numerical experiments indicate that the results hold for more general curved and mixed meshes. These operators also have applications in the context of coarsening solution fields defined on meshes with nonconforming refinement. The transfer operators for H^1 finite element spaces require a globally coupled solve, for which robust and efficient preconditioners are developed. We present several numerical results confirming our analysis and demonstrate the utility of the new mappings in the context of adaptive mesh refinement and conservative multi-discretization coupling.



There are no comments yet.


page 1

page 2

page 3

page 4


Non-Conforming Mesh Refinement for High-Order Finite Elements

We propose a general algorithm for non-conforming adaptive mesh refineme...

Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures

The Landau collision integral is an accurate model for the small-angle d...

H^1-Stability of the L^2-Projection onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes

The L^2-orthogonal projection Π_h:L^2(Ω)→𝕍_h onto a finite element (FE) ...

High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes

In mixed finite element approximations of Hodge Laplace problems associa...

The Effect of Data Transformations on Scalar Field Topological Analysis of High-Order FEM Solutions

High-order finite element methods (HO-FEM) are gaining popularity in the...

Residual stresses in metal deposition modeling: discretizations of higher order

This article addresses the research question if and how the finite cell ...

Acceleration of tensor-product operations for high-order finite element methods

This paper is devoted to GPU kernel optimization and performance analysi...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.