Related papers: High-order Finite Element--Integral Equation Coupl…
In this paper, we introduce an immersed $C^0$ interior penalty method for solving two-dimensional biharmonic interface problems on unfitted meshes. To accommodate the biharmonic interface conditions, high-order immersed finite element (IFE)…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
This work presents a multigrid preconditioned high order immersed finite difference solver to accurately and efficiently solve the Poisson equation on complex 2D and 3D domains. The solver employs a low order Shortley-Weller multigrid…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…
We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…
We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
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…
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…
The particle-in-cell (PIC) method has been widely used for plasma simulation, because of its noise-reduction capability and moderate computational cost. The immersed finite element (IFE) method is efficient for solving interface problems on…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite…
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…
In this paper, we study arbitrary order extended finite element (XFE) methods based on two discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and three dimensions. Optimal error estimates in the…