Related papers: Finite element approximations of minimal surfaces:…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems with heterogeneous coefficients. The local approximation…
A mesh improvement methodology is pre- sented which aims to improve the quality of the worst elements in 3D meshes with non-planar surfaces which cannot be improved using traditional methods. A nu- merical optimisation algorithm, which…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of available a posteriori error estimates as well as a state-of-the-art…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…
We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of…
We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…
An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in $\mathbb{R}^3$ is obtained. This Mergelyan type result can be extended to the family of complete minimal surfaces of weak finite total…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…