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To understand how magma propagates in the crust, displacement data are analyzed using models combined with inversions. Most often, the fracture geometry is assumed and discretized into dislocations, whose amplitude is determined by linear inversions. However, determination of dislocations is not as physical and parsimonious as determination of stress changes. In addition, most dislocation solutions assume that the Earth is an elastic and homogeneous half-space, which can lead to inaccurate results, as volcanoes are intrinsically heterogeneous (Montgomery-Brown et al., 2009; Masterlark, 2007).To resolve pressure instead of dislocations, a method (Smittarello et al., 2019a and 2019b) was previously implemented that relied on the combination of InSAR and GNSS data, where InSAR data covering an eruption were used to determine the geometry of the eruptive fracture and GNSS data were used to track the pressurized part of this fracture. This method was applied to the May 2016 Piton de la Fournaise (Réunion Island, France) eruption, showing that magma first intruded in a sill before turning into the dike that fed the eruption.In order to take medium heterogeneities into account, we propose a new method (Dabaghi et al., 2026) based on a fictitious domains approach (Bodart et al., 2016). As we use finite elements, heterogeneous media can be taken into account. The cost function involves a misfit, as well as regularization terms. An algorithm is presented based on the direct problem and the adjoint problem. Synthetic tests demonstrate that the method is efficient and robust for one to four InSAR observations in different lines of sight, even in the presence of missing data and noise. The method also works for GNSS data. Finally, our method was tested on the May 2016 eruption of Piton de la Fournaise, showing results consistent with our previous analysis, providing further validation.