Related papers: A Novel Scaled Boundary Finite Element Method in C…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…
We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…
We design a cut finite element method for the incompressible Stokes equations on curved domains. The cut finite element method allows for the domain boundary to cut through the elements of the computational mesh in a very general fashion.…
A finite element method is introduced to track interface evolution governed by the level set equation. The method solves for the level set indicator function in a narrow band around the interface. An extension procedure, which is essential…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment.…