17 citations · 55 across the 7 of their papers we have counts for
7 papers
The concept of mapped coercivity for nonlinear operators in Banach spaces
Roland Becker, Malte Braack
We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypothes…
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite…
Goal-oriented adaptive finite element method for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite elemen…
Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems
Roland Becker, Michael Innerberger, Dirk Praetorius
We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on thi…
Goal-oriented adaptive finite element methods with optimal computational complexity
Roland Becker, Gregor Gantner, Michael Innerberger +1
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-r…
Optimal convergence rates for goal-oriented FEM with quadratic goal functional
Roland Becker, Michael Innerberger, Dirk Praetorius
We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal fun…
Finite element formulation of general boundary conditions for incompressible flows
Roland Becker, Daniela Capatina, Robert Luce +1
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts…