A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.

This paper presents an application of the element agglomeration-based coarsening procedure (agglomeration AMGe) proposed in [10], to build the components of a multigrid method for solving nonlinear finite element elliptic equations on general unstructured meshes. The agglomeration-based AMGe offers the ability to define coarse elements and element matrices, provided access to elements and eleme...

Keywords: Nonlinear integro-differential equations Finite elements Galerkin method a b s t r a c t Galerkin finite element method for the approximation of a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. First type initial-boundary value problem is investigated. The convergence of the finite element scheme is proved. The ...

We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.

This paper is concerned with the finite element method for nonlinear Hamiltonian systems from three aspects: conservation of energy, symplicity, and the global error. To study the symplecticity of the finite element methods, we use an analytical method rather than the commonly used algebraic method. We prove optimal order of convergence at the nodes tn for mid-long time and demonstrate the symp...

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolati...

A Finite Element Method for Fully Nonlinear Water Waves Xing Cai,∗ Hans Petter Langtangen,† Bjørn Fredrik Nielsen,∗ and Aslak Tveito∗ ∗Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, N-0316, Oslo, Norway; and †Mechanics Division, Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316, Oslo, Norway E-mail: [email protected], [email protected], bjornn@i...

In this study, we present a model based on the “second-order” nonlinear homogenization method for estimating the macroscopic response and the evolution of microstructure in two-dimensional viscoplastic porous media. The estimates of the new model are compared with unit cell finite element calculations and the earlier “variational” nonlinear homogenization method. The three methods are compared ...

A finite element method for steady-state viscous incompressible thermal flows has been developed. The finite element equations are derived from a set of coupled nonlinear Navier-Stokes equations that consists of the conservation of mass, momentum, and energy equations. These derived finite element equations are validated by developing a corresponding finite element computer program that can be ...

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method...