Higher-order difference and higher-order splitting methods for 2D parabolic problems with mixed derivatives

Higher-Order Difference and Higher-Order Splitting Methods for 2D Parabolic Problems with Mixed Derivatives

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...

Higher-order operator splitting methods for deterministic parabolic equations

Mixed Fem of Higher Order for Contact Problems with Friction

This paper presents a mixed variational formulation and its discretization by finite elements of higher-order for the Signorini problem with Tresca friction. To guarantee the unique existence of the solution to the discrete mixed problem, a discrete inf-sup condition is proved. Moreover, a solution scheme based on the dual formulation of the problem is proposed. Numerical results confirm the th...

Boundary Value Problems for Higher Order Parabolic Equations

We consider a constant coefficient parabolic equation of order 2m and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order m−1 lie in L2 with respect to surface measure. In addition, a regularity result for the solution is obtained if...

Strehl Ratio with Higher-Order Parabolic Filter