40 citations · 51 across the 6 of their papers we have counts for
11 papers
Residual growth control for general maps and an approximate inverse function result
Mario Amrein
The need to control the residual of a potentially nonlinear function arises in several situations in mathematics. For example, computing the zeros of a given map, or…
A numerical energy minimisation approach for semilinear diffusion-reaction boundary value problems based on steady state iterations
Mario Amrein, Pascal Heid, Thomas P. Wihler
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational sch…
Linearized Continuous Galerkin hp-FEM Applied to Nonlinear Initial Value Problems
Mario Amrein
In this note we consider the continuous Galerkin time stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we de…
A Global Newton-Type Scheme Based on a Simplified Newton-Type Approach
Mario Amrein
Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step…
Adaptive Newton-Type Schemes Based on Projections
Mario Amrein
In this work we present and discuss a possible globalization concept for Newton-type methods. We consider nonlinear problems in using the concepts from or…
Adaptive Fixed Point Iterations for Semilinear Elliptic Partial Differential Equations
Mario Amrein
In this paper we study the behavior of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space sett…
Adaptive Pseudo-Transient-Continuation-Galerkin Methods for Semilinear Elliptic Partial Differential Equations
Mario Amrein, Thomas P. Wihler
In this paper we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with p…
An Adaptive Newton-Method Based on a Dynamical Systems Approach
Mario Amrein, Thomas P. Wihler
The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possi…
An -Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems
Mario Amrein, Jens M. Melenk, Thomas P. Wihler
In this paper we develop an -adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations.…
Fully Adaptive Newton-Galerkin Time Stepping Methods for Singularly Perturbed Parabolic Evolution Equations
Mario Amrein, Thomas P. Wihler
In this paper we develop an adaptive procedure for the numerical solution of semilinear parabolic problems, with possible singular perturbations. Our approach combines a linearizat…
Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations
Mario Amrein, Thomas P. Wihler
In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both…