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In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…

Numerical Analysis · Mathematics 2022-12-21 Bangti Jin , Xiliang Lu , Qimeng Quan , Zhi Zhou

We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…

Numerical Analysis · Mathematics 2017-04-04 Markus Bachmayr , Albert Cohen , Wolfgang Dahmen

In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…

Numerical Analysis · Mathematics 2023-08-08 Shafqat Ali , Francesco Ballarin , Gianluigi Rozza

We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…

Numerical Analysis · Mathematics 2026-05-11 Brendan Keith , Frédéric Marazzato

We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…

Numerical Analysis · Mathematics 2026-02-26 Franco Dassi , Rekha Khot , Andres E. Rubiano , Ricardo Ruiz-Baier

In the present work, we consider weakly-singular integral equations arising from linear second-order strongly-elliptic PDE systems with constant coefficients, including, e.g., linear elasticity. We introduce a general framework for optimal…

Numerical Analysis · Mathematics 2022-04-29 Gregor Gantner , Dirk Praetorius

This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

Optimization and Control · Mathematics 2022-08-30 Bastien Chaudet-Dumas

In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linear kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is…

Numerical Analysis · Mathematics 2024-01-18 Patrick Bammer , Lothar Banz , Andreas Schröder

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…

Graphics · Computer Science 2022-07-26 Sebastian Weiss , Robert Maier , Rüdiger Westermann , Daniel Cremers , Nils Thuerey

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Renzo Mosetti , Gianluigi Rozza

Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…

Soft Condensed Matter · Physics 2025-08-28 JiaHao Li , Weicheng Huang , YinBo Zhu , Luxia Yu , Xiaohao Sun , Mingchao Liu , HengAn Wu

We consider the a posteriori error analysis of fully discrete approximations of parabolic problems based on conforming $hp$-finite element methods in space and an arbitrary order discontinuous Galerkin method in time. Using an equilibrated…

Numerical Analysis · Mathematics 2018-12-18 Alexandre Ern , Iain Smears , Martin Vohralik

We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the…

Numerical Analysis · Mathematics 2024-06-21 Philipp Weder , Mariella Kast , Fernando Henríquez , Jan S. Hesthaven

We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…

Numerical Analysis · Mathematics 2014-11-12 Michael Woopen , Georg May , Jochen Schütz

We verify functional a posteriori error estimate proposed by S. Repin for a class of obstacle problems. The obstacle problem is formulated as a quadratic minimization problem with constrains equivalently formulated as a variational…

Numerical Analysis · Mathematics 2014-03-27 Petr Harasim , Jan Valdman

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Optimization and Control · Mathematics 2022-04-20 Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz , Gerd Wachsmuth

We consider the problem of model reduction of parametrized PDEs where the goal is to approximate any function belonging to the set of solutions at a reduced computational cost. For this, the bottom line of most strategies has so far been…

Numerical Analysis · Mathematics 2020-03-02 V. Ehrlacher , D. Lombardi , O. Mula , F. -X. Vialard

This paper addresses the challenge of probabilistic parameter estimation given measurement uncertainty in real-time. We provide a general formulation and apply this to pose estimation for an autonomous visual landing system. We present…

We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic moduli depend on $n$ separated microscopic scales, are random and expressed as a linear expansion of a countable sequence of random variables which are…

Analysis of PDEs · Mathematics 2016-06-29 Viet Ha Hoang , Thanh Chung Nguyen , Bingxing Xia

This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's…

Numerical Analysis · Mathematics 2021-07-22 Mária Lukáčová-Medvid'ová , Hana Mizerová , Hirofumi Notsu , Masahisa Tabata