相关论文: Interior Penalty Mixed Finite Element Methods of A…
We consider mixed finite element methods with exact symmetric stress tensors. We derive a new quasi-optimal a priori error estimate uniformly valid with respect to the compressibility. For the a posteriori error analysis we consider the…
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…
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…
In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…
This paper develops stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
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…
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…
A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div)-Pk…
In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…
In this paper, we present a study on the effect of penalty term in the mixed Discontinuous Galerkin Finite Element Method for the biharmonic equation proposed by \cite{gudi2008mixed}. The proposed mixed Discontinuous Galerkin Method showed…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
The present paper proposes and analyzes an interior penalty technique using $C^0$-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the…
A new family of mixed finite element methods$-$compatible-strain mixed finite element methods (CSFEMs)$-$are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu-Washizu-type functional is extremized…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…