An alternative method for solving direct and inverse Stokes problems.
An Analysis of a Mixed Finite Element Method for the Navier-Stokes Equations.
An analysis of electrical impedance tomography with applications to Tikhonov regularization
This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in Lp-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov...
An analysis of stability concepts for the Navier-Stokes equations.
An analysis of the boundary layer in the 1D surface Cauchy–Born model
The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...
An analysis of the boundary layer in the 1D surface Cauchy–Born model∗
The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...
An analysis of the cell vertex method
An analysis of the convergence of mixed finite element methods
An Analysis of the p-Version of the Finite Element Method for Nearly Incompressible Materials. Uniformly Valid, Optimal Error Estimates
An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
An analysis technique for stabilized finite element solution of incompressible flows
This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the stability of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.
An analysis technique for stabilized finite element solution of incompressible flows
This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the sta bi li ty of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.
An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach...
An analytical approach for quasi-linear equation in second order.
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab)...
An application of the finite element method for solving the system of partial differential equations
An application of the finite element method for solving the system of partial differential equations
An Approximation Technique for the Numerical Solution of a Stefan Problem.
An Asymptotic Finite Element Method for Improvement of Solutions of Boundary Layer Problems.
An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in two dimensions.