We present multigrid methods for a biharmonic problem with boundary conditions of the Cahn-Hilliard type. These multigrid methods are based on discretizations obtained by a quadratic C interior penalty method. Since the finite element space is a standard space for second order problems, multigrid solves for second order problems can be used naturally in the smoothing steps. We will present theo...

We study a two-level additive Schwarz preconditioner for C0 interior penalty 7 methods for a biharmonic problem with essential and natural boundary conditions with Cahn8 Hilliard type. We show that the condition number of the preconditioned system is bounded 9 by C(1+(H3/δ 3)), where H is the typical diameter of a subdomain, δ measures the overlap 10 among the subdomains, and the positive const...

Abstract Seeking efficient solutions to nonlinear boundary value problems is a crucial challenge in the mathematical modelling of many physical phenomena. A well-known example this solving Biharmonic equation relating numerous fluid and solid mechanics. One must note that, general, it challenging solve such due higher-order partial derivatives differential operators. An artificial neural networ...

In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.

The Phox homology domain (PX domain) is a phosphoinositide-binding structural domain that is critical in mediating protein and cell membrane association and has been found in more than 100 eukaryotic proteins. The abundance of PX domains in nature offers an opportunity to redesign the protein using EvoDesign, a computational approach to design new sequences based on structure profiles of multip...

In this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted Dirichlet spaces or Bloch type spaces to $Q_K$ type spaces.

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk D in C arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of t...