
Nonsymmetric isogeometric FEMBEM couplings
We present a coupling of the Finite Element and the Boundary Element Met...
read it

Convergence rate of DeepONets for learning operators arising from advectiondiffusion equations
We present convergence rates of operator learning in [Chen and Chen 1995...
read it

Parameter dependent finite element analysis for ferronematics solutions
This paper focuses on the analysis of a free energy functional, that mod...
read it

Convergence Rates for Projective Splitting
Projective splitting is a family of methods for solving inclusions invol...
read it

Applications of the BackusGilbert method to linear and some non linear equations
We investigate the use of a functional analytical version of the Backus...
read it

First order strong approximation of AitSahaliatype interest rate model with Poisson jumps
For AitSahaliatype interest rate model with Poisson jumps, we are inte...
read it

Fluxmortar mixed finite element methods on nonmatching grids
We investigate a mortar technique for mixed finite element approximation...
read it
The JohnsonNédélec FEMBEM Coupling for magnetostatic problems in the isogeometric framework
We consider a JohnsonNédélec FEMBEM coupling, which is a direct and nonsymmetric coupling of finite and boundary element methods, in order to solve interface problems for the magnetostatic Maxwell's equations with the magnetic vector potential ansatz. In the FEMdomain, equations may be nonlinear, whereas they are exclusively linear in the BEMpart to guarantee the existence of a fundamental solution. First, the weak problem is formulated in quotient spaces to avoid resolving to a saddle point problem. Second, we establish in this setting wellposedness of the arising problem using the framework of Lipschitz and strongly monotone operators as well as a stability result for a special type of nonlinearity, which is typically considered in magnetostatic applications. Then, the discretization is performed in the isogeometric context, i.e., the same type of basis functions that are used for geometry design are considered as ansatz functions for the discrete setting. In particular, NURBS are employed for geometry considerations, and BSplines, which can be understood as a special type of NURBS, for analysis purposes. In this context, we derive a priori estimates w.r.t. hrefinement, and point out to an interesting behavior of BEM, which consists in an amelioration of the convergence rates, when a functional of the solution is evaluated in the exterior BEMdomain. This improvement may lead to a doubling of the convergence rate under certain assumptions. Finally, we end the paper with a numerical example to illustrate the theoretical results, along with a conclusion and an outlook.
READ FULL TEXT
Comments
There are no comments yet.