What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Finite element method
- Partial differential equation
His main research concerns Finite element method, Mathematical analysis, Applied mathematics, Discretization and A priori and a posteriori.
His Finite element method study focuses on Galerkin method in particular.
His work in Mathematical analysis covers topics such as Navier stokes which are related to areas like Compatibility.
As part of his studies on Applied mathematics, Rolf Rannacher frequently links adjacent subjects like Mixed finite element method.
Rolf Rannacher combines subjects such as Multigrid method, Stiffness matrix, Numerical partial differential equations and Extended finite element method with his study of Mixed finite element method.
His study in Error detection and correction is interdisciplinary in nature, drawing from both Norm, Control theory and Eigenfunction.
His most cited work include:
- An optimal control approach to a posteriori error estimation in finite element methods (984 citations)
- Finite element approximation of the nonstationary Navier-Stokes problem. I : Regularity of solutions and second-order error estimates for spatial discretization (631 citations)
- Finite-element approximations of the nonstationary Navier-Stokes problem. Part IV: error estimates for second-order time discretization (536 citations)
What are the main themes of his work throughout his whole career to date?
Rolf Rannacher mainly focuses on Finite element method, Applied mathematics, Discretization, Mathematical analysis and Mathematical optimization.
His study on Mixed finite element method, Galerkin method and Method of mean weighted residuals is often connected to A priori and a posteriori as part of broader study in Finite element method.
In his research, Computation is intimately related to Compressibility, which falls under the overarching field of Applied mathematics.
Rolf Rannacher interconnects Laminar flow, Linearization, Multigrid method, Navier–Stokes equations and Pointwise in the investigation of issues within Discretization.
The study incorporates disciplines such as Boundary element method and Navier stokes in addition to Mathematical analysis.
The concepts of his Mathematical optimization study are interwoven with issues in Mesh generation and Polygon mesh.
He most often published in these fields:
- Finite element method (52.11%)
- Applied mathematics (39.44%)
- Discretization (29.58%)
What were the highlights of his more recent work (between 2009-2018)?
- Finite element method (52.11%)
- Discretization (29.58%)
- Applied mathematics (39.44%)
In recent papers he was focusing on the following fields of study:
Rolf Rannacher focuses on Finite element method, Discretization, Applied mathematics, Mathematical optimization and Method of mean weighted residuals.
His work carried out in the field of Finite element method brings together such families of science as Numerical analysis and Mathematical analysis.
His research in the fields of Boundary value problem and Dirichlet eigenvalue overlaps with other disciplines such as Poincaré–Steklov operator.
His Discretization research is multidisciplinary, incorporating elements of Linear differential equation, Nonlinear system, Optimal control, Eigenvalues and eigenvectors and Ode.
He has researched Applied mathematics in several fields, including Engineering mathematics and Computational mechanics.
In the subject of general Mathematical optimization, his work in Duality, Constrained optimization and Optimization problem is often linked to A priori and a posteriori, thereby combining diverse domains of study.
Between 2009 and 2018, his most popular works were:
- Error Analysis for a Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems (65 citations)
- Adaptive Galerkin Finite Element Methods for the Wave Equation (50 citations)
- Goal‐oriented space–time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow (47 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Partial differential equation
- Finite element method
His scientific interests lie mostly in Finite element method, Discretization, Mixed finite element method, Applied mathematics and Mathematical analysis.
His work in the fields of Finite element method, such as Galerkin method and Temporal discretization, intersects with other areas such as A priori and a posteriori.
His Discretization study combines topics from a wide range of disciplines, such as Linear differential equation, Basis, Lyapunov stability and Ode.
He has included themes like Inverse iteration, Eigenvalues and eigenvectors, Dirichlet eigenvalue and Finite element solution in his Mixed finite element method study.
Rolf Rannacher works mostly in the field of Applied mathematics, limiting it down to topics relating to Mathematical optimization and, in certain cases, Mathematical problem and Range, as a part of the same area of interest.
His work on Dirichlet boundary condition, Boundary value problem and Dirichlet's principle as part of general Mathematical analysis study is frequently connected to Poincaré–Steklov operator and Elliptic boundary value problem, therefore bridging the gap between diverse disciplines of science and establishing a new relationship between them.
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