相关论文: A Higher Order Isoparametric Fictitious Domain Met…
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
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…
The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary…
Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains…
We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty…
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogous of the normal derivative…
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functions representing by deep neural networks are…
The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to the physical boundary. The method combines an isoparametric…
In this paper we consider the finite element approximation of Maxwell's problem and analyse the prescription of essential boundary conditions in a weak sense using Nitsche's method. To avoid indefiniteness of the problem, the original…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…