Measure Data and Numerical Schemes for Elliptic Problems

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Monotone schemes for a class of nonlinear elliptic and parabolic problems

We construct monotone numerical schemes for a class of nonlinear PDE for elliptic and initial value problems for parabolic problems. The elliptic part is closely connected to a linear elliptic operator, which we discretize by monotone schemes, and solve the nonlinear problem by iteration. We assume that the elliptic differential operator is in the divergence form, with measurable coefficients s...

Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems

Biorthogonal wavelet-based full-approximation schemes are introduced in this paper for the numerical solution of elasto-hydrodynamic lubrication line and point contact problems. The proposed methods give higher accuracy in terms of better convergence with low computational time, which have been demonstrated through the illustrative problems.

Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional

First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectivene...