The signed distance function d to an embedded (hyper-) surface Γ is required in the analysis and implementation of some higher order methods for the numerical treatment of partial differential equations on surfaces. Two algorithms for the approximation of d are presented in this paper, which only require a finite element approximation of a (smooth) level set function of Γ. One method is based o...

In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim proble...

Two-level finite element methods are applied to solve numerically the 2D/3D steady Navier-Stokes equations if a strong uniqueness condition ( ‖f‖ −1 ‖f‖0 ) 1 2 ≤ δ = 1 − N‖f‖ −1 ν2 holds, where N is defined in (2.4)-(2.6). Moreover, one-level finite element method is applied to solve numerically the 2D/3D steady Navier-Stokes equations if a weak uniqueness condition 0 < δ < ( ‖f‖ −1 ‖f‖0 ) 1 2 ...

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which man...

In order to incorporate the credit value adjustment (CVA) in derivative contracts, we propose a set of numerical methods to solve a nonlinear partial differential equation [2] modelling the CVA. Additionally to adequate boundary conditions proposals, characteristics methods, fixed point techniques and finite elements methods are designed and implemented. A numerical test illustrates the behavio...