Biochar can increase the stable C content of soil. However, studies on the longer-term role
of plant–soil–biochar interactions and the consequent changes to native soil organic carbon …

This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …

There is a knowledge gap on biochar carbon (C) longevity and its priming effects on soil
organic carbon (SOC) and recent root-derived C under field conditions. This knowledge …

Stochastic Galerkin approximation is an increasingly popular approach for the solution of
elliptic PDE problems with correlated random data. A typical strategy is to combine …

This paper is concerned with the design and implementation of efficient solution algorithms
for elliptic PDE problems with correlated random data. The energy orthogonality that is built …

We analyze the convergence of probability density functions utilizing approximate models
for both forward and inverse problems. We consider the standard forward uncertainty …

Organo-mineral interactions control the stabilisation of soil organic matter (SOM) in mineral
soils. Biochar can enhance these interactions via a range of mechanisms including Al …

Generalized polynomial chaos (gPC) expansions are a powerful tool for studying differential
equations with random coefficients, allowing, in particular, one to efficiently approximate …

We use the ideas of goal-oriented error estimation and adaptivity to design and implement
an efficient adaptive algorithm for approximating linear quantities of interest derived from …

We develop computable a posteriori error estimates for the pointwise evaluation of linear
functionals of a solution to a parameterized linear system of equations. These error …