A parabolic-hyperbolic system modelling a moving cell.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
A partial regularity result for a class of stationary Yang-Mills in high dimension.
We prove, for arbitrary dimension of the base n greater than or equal to 4, stationary Yang-Mills Fields satisfying Borne approximability property are regular apart from a closed subset of the base having zero (n-4)- Hausdorff measure.
A partial solution for Feynman's problem – a new derivation of the Weyl equation.
A Particle Method to Solve the Navier-Stokes System.
A Penalty Method for the Approximate Solution of Stationary Maxwell Equations.
A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation
We consider the finite element method for the time-dependent Stokes problem with the slip boundary condition in a smooth domain. To avoid a variational crime of numerical computation, a penalty method is introduced, which also facilitates the numerical implementation. For the continuous problem, the convergence of the penalty method is investigated. Then we study the fully discretized finite element approximations for the penalty method with the P1/P1-stabilization or P1b/P1 element. For the discretization...
A piecewise P2-nonconforming quadrilateral finite element
We introduce a piecewise P2-nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element space is defined by the set of all piecewise P2-polynomials that are quadratic in each triangle and continuously differentiable on the quadrilateral. The degrees of freedom (DOFs) are defined by the eight values at the two Gauss points on each of the four edges plus the value at the intersection of the...
A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations
We prove a posteriori error estimates of optimal order for linear Schrödinger-type equations in the L∞(L2)- and the L∞(H1)-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis et al. in [Math. Comput. 75 (2006) 511–531], leads to a posteriori upper bounds that are of optimal order in the L∞(L2)-norm, but of suboptimal order in the L∞(H1)-norm. The optimality in the case of L∞(H1)-norm is recovered by using...
A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations*
We prove a posteriori error estimates of optimal order for linear Schrödinger-type equations in the L∞(L2)- and the L∞(H1)-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis et al. in [Math. Comput.75 (2006) 511–531], leads to a posteriori upper bounds that are of optimal order in the L∞(L2)-norm, but of suboptimal order in the L∞(H1)-norm. The optimality in the case of L∞(H1)-norm is recovered by using...
A posteriori error estimates for nonlinear problems. -estimates for finite element discretizations of elliptic equations
A Posteriori Error Estimators for the Stokes Equations.
A predator-prey model with combined death and competition terms
The existence of a positive solution for the generalized predator-prey model for two species are investigated. The techniques used in the paper are the elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties of the solution of logistic equations.
A Priori Estimates and a Liouvielle Theorem for Complex Monge-Ampère Equations.
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
A problem in Rayleigh-Taylor instability
A problem related to the Hall effect in a semiconductor with an electrode of an arbitrary shape.
A Pseudo-Algebra of Observables for the Dirac Equation.
A pseudoconformal compactification of the nonlinear Schrödinger equation and applications.
A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation