# Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

This work focuses on the development of a non-conforming domain decomposition method for the approximation of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a discrete number of Lagrange multipliers defined over the interfaces of adjacent subdomains. The method falls into the class of primal hybrid methods, which also include the well-known mortar method. Differently from the mortar method, we discretize the space of basis functions on the interface by spectral approximation independently of the discretization of the two adjacent domains; one of the possible choices is to approximate the interface variational space by Fourier basis functions. As we show in the numerical simulations, our approach is well-suited for the solution of problems with non-conforming meshes or with finite element basis functions with different polynomial degrees in each subdomain. Another application of the method that still needs to be investigated is the coupling of solutions obtained from otherwise incompatible methods, such as the finite element method, the spectral element method or isogeometric analysis.

## Authors

• 5 publications
• 3 publications
06/05/2021

### A finite element method for two-phase flow with material viscous interface

This paper studies a model of two-phase flow with an immersed material v...
12/27/2018

### Isogeometric Mortar Coupling for Electromagnetic Problems

This paper discusses and analyses two domain decomposition approaches fo...
01/03/2022

### Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains

We consider the problem of domain approximation in finite element method...
08/08/2017

### Modelling of a Permanent Magnet Synchronous Machine Using Isogeometric Analysis

Isogeometric analysis (IGA) is used to simulate a permanent magnet synch...
11/17/2020

### A novel equi-dimensional finite element method for flow and transport in fractured porous media satisfying discrete maximum principle and conservation properties

Numerical simulations of flow and transport in porous media usually rely...
01/04/2021

### Optimization and variational principles for the shear strength reduction method

This paper is focused on the definition, analysis and numerical solution...
07/28/2020

### A projected super-penalty method for the C^1-coupling of multi-patch isogeometric Kirchhoff plates

This work focuses on the development of a super-penalty strategy based o...
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